Simulación de Variables Aleatorias no uniformes en R
Jader Torres
2025-09-17
1. Llegadas de solicitudes
Suponga que, en promedio, llegan 5 solicitudes por hora al sistema. a. Genere 5000 valores aleatorios que representen el número de solicitudes que llegan en cada hora. b. Interprete el resultado. c. Realice un gráfico de barras de las frecuencias. d. Determine la probabilidad impírica de lleguen menos de 3 solicitudes
set.seed(1610)
solicitudes<-rpois(5000,5)
solicitudes## [1] 6 4 8 6 8 8 5 5 4 5 6 7 7 5 9 4 2 6 6 6 4 5 9 8
## [25] 2 8 5 5 5 4 8 3 2 3 4 4 7 5 7 1 4 2 3 4 4 5 9 8
## [49] 5 7 7 2 4 6 5 1 2 6 2 6 4 1 4 7 3 9 5 7 5 4 6 5
## [73] 7 3 8 1 6 4 11 7 3 7 5 4 3 6 3 7 6 5 1 6 2 7 3 6
## [97] 7 4 7 4 5 3 2 2 2 3 5 5 5 3 7 11 2 0 7 3 8 1 5 4
## [121] 6 5 4 2 2 3 3 5 6 5 3 2 7 2 5 4 6 4 5 4 3 11 4 8
## [145] 7 2 3 4 8 4 6 5 5 4 8 4 5 10 5 6 7 3 7 4 5 4 4 4
## [169] 8 6 3 3 11 3 6 1 5 5 5 9 5 3 6 10 4 10 6 5 5 7 6 5
## [193] 6 7 6 3 6 5 5 6 5 7 7 4 4 5 1 5 3 3 5 9 7 1 2 5
## [217] 7 6 7 11 5 4 7 5 3 6 2 10 10 5 6 3 5 7 6 6 8 3 7 6
## [241] 1 5 6 3 5 4 5 5 4 2 4 4 7 10 3 3 4 2 10 7 11 5 4 5
## [265] 5 5 4 7 6 4 6 6 5 3 5 6 4 4 4 5 9 6 5 6 6 6 5 7
## [289] 9 2 3 8 5 4 5 8 1 8 5 2 8 7 1 5 4 9 7 4 1 1 3 5
## [313] 7 1 6 8 5 6 3 2 4 2 4 5 6 3 7 3 5 2 3 1 5 3 5 6
## [337] 4 5 5 4 11 3 4 12 0 9 3 6 2 4 6 4 4 6 0 4 3 6 6 9
## [361] 4 1 6 11 3 7 5 5 4 4 4 7 3 8 6 6 6 3 6 5 5 5 5 6
## [385] 4 6 4 8 3 6 5 4 1 3 2 3 3 6 5 5 6 5 6 5 3 5 2 5
## [409] 10 5 5 3 8 4 6 7 2 4 8 2 3 4 7 5 8 7 3 4 4 4 7 5
## [433] 5 5 3 10 6 6 3 10 2 7 4 6 3 7 7 4 4 8 5 3 6 7 7 3
## [457] 8 3 6 5 5 8 2 4 2 3 8 4 5 6 6 2 7 7 4 2 3 7 5 5
## [481] 5 7 4 8 2 3 7 10 2 2 3 6 4 4 4 6 2 7 8 6 5 3 1 9
## [505] 6 4 5 7 5 7 6 7 3 4 6 6 5 1 5 2 3 5 10 10 1 3 3 6
## [529] 3 2 6 7 5 7 8 3 8 4 10 5 4 7 4 10 2 6 8 5 4 6 13 2
## [553] 9 6 4 3 2 4 7 7 2 4 1 5 2 5 6 3 10 4 9 3 8 3 2 8
## [577] 9 5 9 3 5 5 6 3 8 7 4 6 7 6 6 5 4 2 3 1 6 2 9 5
## [601] 3 4 4 5 5 2 10 8 3 8 6 3 2 4 2 7 4 3 6 5 6 4 3 9
## [625] 4 5 2 4 2 8 8 4 9 7 2 4 8 3 5 3 7 4 10 7 3 5 3 7
## [649] 6 4 5 7 7 6 2 2 7 6 6 7 5 5 3 9 5 7 5 2 4 6 6 4
## [673] 3 4 3 1 4 7 6 7 5 4 1 2 2 7 6 5 7 2 4 8 7 6 9 5
## [697] 6 9 5 5 9 5 7 2 6 9 7 5 4 7 3 5 2 5 5 2 4 8 0 5
## [721] 9 5 6 5 7 4 7 2 6 4 6 3 3 5 4 11 2 3 2 8 4 2 11 1
## [745] 1 4 2 4 4 3 4 8 7 6 6 4 7 4 2 3 5 9 8 5 2 4 5 2
## [769] 3 3 4 3 7 4 2 4 7 6 5 3 3 3 6 3 4 5 6 7 4 6 9 1
## [793] 8 3 4 5 5 2 8 9 1 5 5 6 5 7 4 3 4 6 9 3 6 4 3 5
## [817] 7 7 4 2 11 4 7 7 4 4 3 3 6 5 7 3 5 5 4 3 10 5 8 9
## [841] 6 3 10 4 5 7 5 4 6 4 6 4 7 5 3 6 4 10 6 1 6 9 7 2
## [865] 7 1 4 6 6 6 6 10 6 3 6 5 5 3 5 4 5 5 4 3 5 6 4 5
## [889] 5 4 5 5 1 4 4 8 9 7 2 1 4 3 7 4 5 2 4 2 4 6 4 5
## [913] 2 4 7 4 6 4 4 4 10 4 5 3 2 6 6 5 6 6 6 4 5 3 4 6
## [937] 2 7 6 7 6 2 5 2 3 4 3 6 9 8 4 6 4 2 5 6 5 8 2 2
## [961] 5 1 5 3 7 4 5 4 6 4 9 2 6 2 3 8 2 5 2 6 9 4 4 3
## [985] 4 3 2 6 7 5 5 5 8 8 3 6 6 3 6 8 5 3 3 5 4 2 3 0
## [1009] 4 6 5 1 6 5 3 8 7 5 5 3 4 3 7 5 7 8 6 5 7 5 9 9
## [1033] 5 5 5 5 3 7 3 2 3 4 2 9 8 7 11 3 3 6 2 7 9 8 4 3
## [1057] 6 5 3 6 6 4 3 6 6 5 1 2 3 8 5 6 5 8 5 1 2 7 7 8
## [1081] 4 4 5 1 5 5 4 4 1 3 6 2 5 6 4 1 6 2 7 6 3 7 5 6
## [1105] 5 4 6 3 5 4 9 6 5 4 3 2 3 6 4 9 3 7 5 5 7 1 3 6
## [1129] 1 4 3 8 6 6 3 9 2 3 5 7 6 5 5 4 6 4 0 6 5 4 10 4
## [1153] 6 6 4 5 2 5 5 2 4 8 5 3 4 4 4 9 8 6 3 4 4 5 6 7
## [1177] 5 10 2 6 4 4 8 5 5 3 7 6 5 6 3 3 4 2 4 8 4 4 7 3
## [1201] 6 4 2 8 8 5 3 8 4 3 5 2 5 7 7 4 7 10 5 5 5 3 6 5
## [1225] 0 8 4 5 5 4 4 3 4 4 5 5 5 8 4 9 4 5 4 7 9 9 6 8
## [1249] 2 4 15 5 2 7 5 7 7 7 3 4 6 9 5 4 4 2 4 8 6 6 6 2
## [1273] 5 4 5 4 11 2 5 4 3 1 7 1 7 6 5 4 7 6 5 8 10 7 8 5
## [1297] 10 5 2 4 4 2 6 3 1 7 3 6 5 9 4 4 8 5 4 4 4 5 6 8
## [1321] 2 3 7 10 2 4 4 3 3 6 4 11 4 7 9 7 8 11 8 4 5 6 4 10
## [1345] 5 3 4 1 7 3 5 4 5 7 6 2 5 6 3 1 10 3 8 2 5 5 1 2
## [1369] 1 6 4 6 3 7 5 4 2 4 8 5 9 3 4 5 8 8 0 4 3 9 3 6
## [1393] 2 6 6 4 3 5 11 3 4 3 3 6 5 3 4 5 9 1 7 4 2 8 4 3
## [1417] 8 6 4 2 7 4 5 3 4 2 3 4 3 2 4 5 4 7 8 2 5 6 3 4
## [1441] 1 3 2 9 8 5 6 4 3 5 4 6 1 6 1 7 7 6 2 8 4 6 2 3
## [1465] 4 3 7 5 5 5 4 2 10 6 7 2 5 3 3 3 7 4 2 4 5 3 7 4
## [1489] 7 5 2 3 3 3 12 4 7 1 6 2 9 8 4 8 4 4 3 7 6 6 3 8
## [1513] 6 3 3 4 1 7 6 4 4 3 3 4 13 4 5 8 0 11 2 4 6 10 8 5
## [1537] 5 4 5 4 7 6 3 6 7 11 3 8 7 3 0 2 10 6 6 6 4 5 5 6
## [1561] 4 6 7 10 2 4 6 4 9 5 5 9 6 4 4 3 2 5 4 2 4 5 3 4
## [1585] 10 2 5 3 5 2 7 5 8 6 6 1 6 3 4 8 3 6 1 4 8 6 5 3
## [1609] 12 7 6 5 6 12 7 4 12 5 7 4 5 4 7 2 7 2 2 6 6 4 6 3
## [1633] 3 6 5 2 3 8 5 3 5 4 6 8 5 4 5 3 2 7 6 4 3 3 1 5
## [1657] 6 7 1 5 5 3 6 4 4 2 4 5 7 9 4 9 8 6 6 7 9 11 2 4
## [1681] 5 4 4 7 5 4 4 3 11 7 5 8 4 7 9 7 3 4 3 3 3 4 2 1
## [1705] 7 8 2 6 2 2 8 7 5 2 6 3 5 5 4 6 4 2 2 6 1 5 8 1
## [1729] 4 6 4 7 3 6 4 5 8 5 3 6 4 4 9 6 1 5 8 8 2 3 6 3
## [1753] 3 4 3 5 9 6 5 4 6 5 7 6 6 4 4 4 2 5 8 7 2 7 6 3
## [1777] 5 7 7 4 5 7 4 8 4 4 5 2 3 3 6 1 3 4 10 1 3 6 6 10
## [1801] 7 3 7 5 7 2 7 4 4 4 2 6 2 2 3 6 7 4 10 4 7 3 2 5
## [1825] 2 4 4 2 1 6 9 3 2 4 2 6 4 3 2 6 3 3 4 6 2 3 3 4
## [1849] 5 4 4 2 5 0 4 6 4 5 4 4 2 9 7 7 5 4 6 5 4 5 6 6
## [1873] 5 6 4 4 8 7 5 7 9 9 3 6 6 2 3 6 5 10 2 2 4 3 3 1
## [1897] 8 5 6 6 7 8 5 2 3 2 7 5 5 2 3 10 2 2 5 4 7 5 0 7
## [1921] 2 4 6 3 3 4 8 5 7 3 9 8 4 5 3 4 9 3 10 0 2 6 5 2
## [1945] 3 3 1 5 7 5 4 5 7 6 7 5 5 5 9 5 1 5 6 4 5 7 5 8
## [1969] 8 4 9 5 5 7 0 2 8 4 5 4 2 5 3 10 7 11 4 8 8 8 3 5
## [1993] 2 1 4 2 4 7 5 4 7 4 2 4 2 8 5 4 7 4 5 7 9 7 4 3
## [2017] 6 4 10 4 4 6 2 3 4 6 6 2 6 8 7 8 4 3 6 7 4 2 11 6
## [2041] 4 6 4 3 2 7 6 3 2 2 3 5 3 10 2 5 3 11 5 3 4 3 3 3
## [2065] 7 2 6 6 3 9 7 6 5 6 8 2 8 3 0 6 5 3 7 6 4 4 5 5
## [2089] 8 1 9 8 4 10 6 3 6 5 4 0 4 8 6 7 5 6 4 7 4 3 8 3
## [2113] 9 8 5 4 5 8 8 8 8 6 7 11 8 2 5 8 2 5 7 5 9 7 4 4
## [2137] 4 7 8 6 4 5 2 6 2 9 7 8 7 3 6 4 3 6 4 6 5 6 6 3
## [2161] 5 4 2 6 6 4 6 4 4 9 6 5 4 4 17 10 6 7 8 7 5 2 7 4
## [2185] 6 6 5 5 5 4 8 5 5 3 4 6 5 6 7 5 1 3 6 5 4 5 2 5
## [2209] 6 5 8 3 6 4 4 6 5 1 12 4 7 1 7 4 5 9 3 4 5 8 7 5
## [2233] 5 4 3 5 5 6 7 5 7 4 4 3 6 5 2 1 7 6 2 2 5 2 2 6
## [2257] 6 4 3 7 5 4 7 5 6 5 11 3 6 2 3 6 6 5 5 1 5 7 7 4
## [2281] 9 3 1 7 6 2 3 2 5 5 7 6 6 2 3 2 4 4 5 3 4 3 6 3
## [2305] 7 7 5 7 4 4 8 4 2 5 2 3 8 6 5 3 5 7 7 8 6 6 6 5
## [2329] 10 4 6 3 3 7 4 2 3 6 6 2 7 2 2 6 4 4 3 6 6 3 4 4
## [2353] 6 5 7 5 4 7 9 7 6 7 4 3 6 7 7 8 8 3 7 5 4 7 3 4
## [2377] 2 5 2 5 4 3 3 3 6 6 4 2 10 5 5 8 3 5 4 7 2 5 4 5
## [2401] 2 4 8 4 4 6 3 7 5 8 3 5 6 4 4 5 4 5 8 7 8 5 5 11
## [2425] 3 3 3 7 4 5 7 4 5 7 4 5 6 8 6 5 5 4 5 3 2 8 5 5
## [2449] 6 3 7 2 6 6 5 10 1 4 3 8 5 5 4 4 2 5 6 9 8 8 4 4
## [2473] 3 6 3 8 7 4 9 5 2 6 5 5 2 3 8 8 4 7 6 4 4 5 2 3
## [2497] 4 2 5 5 5 7 6 6 5 3 7 3 1 5 6 7 2 7 4 8 4 3 3 7
## [2521] 1 5 0 3 4 4 8 12 3 2 4 2 5 5 4 3 7 7 7 7 2 4 2 4
## [2545] 4 4 4 6 7 4 3 4 8 6 4 3 4 4 7 4 4 0 9 9 4 2 6 8
## [2569] 7 7 7 4 2 7 4 3 3 5 5 7 6 5 3 5 5 3 2 5 2 4 7 4
## [2593] 3 9 9 9 8 4 6 5 4 8 6 7 7 4 2 8 2 5 5 9 6 6 1 5
## [2617] 4 4 6 8 7 4 5 1 8 5 6 5 0 8 4 2 7 4 4 4 10 6 5 3
## [2641] 12 7 4 3 6 9 9 3 8 10 9 6 6 6 4 8 5 3 3 10 6 5 3 9
## [2665] 2 2 7 9 3 12 5 5 8 4 3 5 4 4 9 5 1 7 6 5 6 3 9 6
## [2689] 7 2 4 7 8 2 5 7 7 7 3 3 2 5 4 7 4 8 2 8 4 9 4 4
## [2713] 9 5 6 5 5 3 4 3 2 5 5 5 11 7 2 6 6 4 6 6 5 5 6 4
## [2737] 6 7 3 7 6 3 6 7 5 3 5 6 2 3 4 9 2 3 3 1 3 6 6 4
## [2761] 6 4 4 6 7 3 10 7 9 6 6 3 6 6 4 0 7 4 4 6 4 7 5 5
## [2785] 4 3 1 4 10 4 1 8 8 9 5 4 7 5 5 3 6 2 5 2 2 7 4 5
## [2809] 4 8 3 3 2 6 6 6 4 2 8 4 7 4 1 4 2 6 6 5 6 6 3 3
## [2833] 10 7 7 2 1 8 4 3 3 5 4 4 3 5 5 8 7 6 6 5 5 4 4 5
## [2857] 10 5 6 4 7 6 6 4 4 6 4 2 8 3 6 6 8 6 9 6 5 2 7 3
## [2881] 7 7 3 5 5 4 2 0 0 6 6 3 4 2 2 2 4 6 8 8 7 5 4 4
## [2905] 7 6 3 3 2 7 2 1 1 6 4 5 6 8 11 8 2 9 5 6 3 4 5 6
## [2929] 4 5 10 3 4 0 7 4 2 5 5 4 8 6 6 5 1 7 3 6 2 2 7 5
## [2953] 3 11 1 3 6 3 5 9 9 5 7 4 4 4 2 6 4 3 3 3 6 5 6 6
## [2977] 7 5 4 6 6 2 2 4 3 4 3 2 1 7 5 7 6 6 5 7 9 4 2 5
## [3001] 5 11 8 8 3 5 2 10 6 6 6 1 7 1 4 7 3 7 7 7 7 10 4 5
## [3025] 8 4 2 9 3 4 3 2 8 5 6 7 5 3 3 1 6 4 6 5 3 5 6 2
## [3049] 3 5 7 5 8 3 5 5 8 7 4 4 5 5 7 9 6 6 4 1 6 4 6 10
## [3073] 6 6 5 5 2 8 4 5 7 3 6 8 2 4 5 5 3 5 3 6 10 4 2 5
## [3097] 2 9 3 3 3 7 10 4 8 3 6 8 9 3 2 5 1 7 3 7 6 4 6 6
## [3121] 8 6 7 5 9 5 7 7 4 9 4 6 5 1 5 2 6 6 3 4 5 2 4 6
## [3145] 10 5 5 5 5 6 8 2 2 0 2 5 11 4 5 4 9 5 6 3 8 7 9 4
## [3169] 1 3 2 7 4 8 8 8 16 4 5 8 1 5 5 2 9 7 3 3 3 4 6 7
## [3193] 5 5 5 11 4 6 4 5 4 3 3 5 3 6 2 8 4 5 5 5 4 5 5 3
## [3217] 2 6 6 4 4 8 1 2 6 10 5 2 6 3 5 2 5 4 4 3 5 4 8 1
## [3241] 5 4 4 4 5 3 5 4 5 3 6 5 2 7 3 4 3 4 7 5 5 7 4 2
## [3265] 2 3 9 2 5 9 7 4 6 6 3 5 4 4 2 4 6 3 2 7 5 8 5 7
## [3289] 3 1 2 7 0 11 4 3 8 2 6 9 4 4 8 4 5 5 4 4 3 6 7 3
## [3313] 7 9 7 7 2 9 2 7 4 6 3 6 5 1 4 4 8 2 6 6 4 1 5 7
## [3337] 8 9 3 5 5 4 3 4 4 4 3 10 4 6 9 5 8 7 3 5 7 2 4 2
## [3361] 0 5 2 3 10 5 3 8 6 4 1 5 1 3 3 5 3 0 7 1 7 4 5 3
## [3385] 4 6 5 2 2 10 1 5 1 5 6 4 10 1 4 4 6 8 6 6 2 5 5 5
## [3409] 2 5 4 6 5 5 4 6 7 8 2 3 5 4 4 6 5 8 4 3 3 6 3 5
## [3433] 5 5 3 4 2 9 3 6 6 7 6 8 1 3 5 5 8 5 6 5 6 6 8 3
## [3457] 7 6 5 3 3 2 3 6 8 7 3 1 4 4 3 6 8 3 7 3 9 5 3 5
## [3481] 4 3 7 10 7 4 4 1 5 8 6 5 4 4 6 2 1 2 4 4 5 8 5 6
## [3505] 3 1 8 4 6 8 7 6 8 8 3 9 5 3 5 7 5 5 8 7 5 3 4 2
## [3529] 7 3 4 7 3 7 8 5 6 7 10 4 5 3 7 2 0 5 10 3 4 7 6 5
## [3553] 7 8 2 6 5 6 5 11 12 4 2 4 3 7 8 4 5 4 3 2 8 4 10 8
## [3577] 5 7 4 7 4 5 10 11 6 4 3 0 5 3 6 7 2 3 4 7 4 2 4 8
## [3601] 6 4 7 11 7 4 9 8 5 4 0 5 7 5 5 7 8 4 9 7 8 7 5 2
## [3625] 3 3 7 5 3 1 6 2 9 3 5 7 8 2 3 4 6 3 9 1 6 3 7 6
## [3649] 3 5 8 5 8 4 6 4 3 4 5 7 3 3 2 6 4 7 1 7 4 6 3 1
## [3673] 4 2 3 5 2 3 6 4 7 5 3 3 4 3 9 7 4 3 6 3 4 11 7 6
## [3697] 6 1 9 10 4 1 2 2 9 5 8 11 9 1 1 6 3 11 6 3 4 4 9 6
## [3721] 1 2 5 5 5 2 9 4 6 4 6 8 9 6 6 7 5 3 2 3 6 6 4 2
## [3745] 4 6 10 5 5 6 5 6 5 7 2 2 5 7 4 5 3 9 1 7 5 2 8 6
## [3769] 8 3 7 4 4 3 5 4 5 4 5 3 7 7 4 4 5 8 6 8 3 4 13 5
## [3793] 5 5 7 4 5 3 8 7 5 8 6 8 3 5 7 5 7 6 3 5 8 4 2 6
## [3817] 7 2 4 5 5 3 4 4 10 3 3 5 5 6 6 3 3 4 1 3 8 8 5 5
## [3841] 5 2 9 7 2 2 5 2 3 2 3 7 7 5 3 7 3 3 6 6 4 4 7 7
## [3865] 5 4 9 2 10 6 2 3 7 10 4 3 9 9 4 2 5 4 4 8 11 7 6 5
## [3889] 3 4 5 5 1 7 6 4 6 5 5 10 5 5 3 3 6 7 2 4 5 6 2 5
## [3913] 1 2 5 0 7 7 7 4 4 5 8 8 3 6 2 0 6 5 5 3 4 8 6 7
## [3937] 0 4 4 7 10 7 4 10 4 5 9 3 5 5 2 5 2 4 7 3 5 7 7 3
## [3961] 5 4 5 2 7 3 2 3 4 8 5 3 8 8 1 4 3 6 3 3 14 4 7 7
## [3985] 2 5 3 4 5 5 5 2 9 10 5 2 4 2 6 7 4 6 13 5 8 2 6 3
## [4009] 3 6 4 9 4 5 8 7 3 3 6 3 5 6 5 4 8 6 0 6 7 6 2 7
## [4033] 4 6 4 3 6 3 5 3 5 4 7 6 2 10 5 6 5 3 6 10 7 3 4 4
## [4057] 2 6 4 10 3 4 4 4 5 5 4 3 6 7 5 9 6 7 3 9 9 9 8 4
## [4081] 7 3 5 0 0 6 4 4 10 6 4 5 6 3 6 8 3 2 3 3 9 5 5 2
## [4105] 4 2 7 5 3 7 4 7 5 8 2 8 3 5 4 5 11 6 4 5 4 5 6 8
## [4129] 5 6 5 6 8 5 5 2 9 10 2 7 4 6 2 4 3 6 5 3 3 6 7 7
## [4153] 5 3 6 5 1 5 4 10 3 6 1 4 8 7 2 9 4 3 4 6 4 5 3 4
## [4177] 7 8 6 7 4 5 5 5 7 4 6 5 7 5 7 2 3 2 5 8 4 3 3 6
## [4201] 5 7 3 3 7 6 3 6 1 3 7 5 6 10 4 3 6 9 2 5 6 2 4 2
## [4225] 4 3 8 7 4 4 7 4 8 12 5 4 1 5 5 2 6 2 2 2 6 4 4 3
## [4249] 6 5 7 5 4 3 3 3 4 6 7 4 3 7 7 10 9 3 4 3 7 7 9 1
## [4273] 4 7 4 3 8 9 6 11 7 4 4 4 3 5 8 4 5 3 8 5 5 5 4 6
## [4297] 12 6 7 9 4 8 8 7 1 3 6 1 5 5 4 3 3 6 6 3 0 5 5 2
## [4321] 4 6 3 7 4 4 10 1 2 6 5 5 4 9 8 3 3 6 3 4 3 4 4 4
## [4345] 2 6 2 9 2 3 5 4 3 7 2 8 6 9 3 6 7 3 3 6 4 3 5 5
## [4369] 7 4 2 2 3 4 8 8 4 3 5 2 8 11 4 4 3 7 8 5 3 3 7 5
## [4393] 7 4 6 5 6 6 4 1 6 3 4 3 5 6 3 5 5 10 9 3 5 4 2 4
## [4417] 7 4 2 9 3 1 4 7 6 4 2 3 4 4 1 7 5 5 8 6 7 3 3 4
## [4441] 4 5 2 2 6 6 2 9 6 1 8 6 6 7 3 5 7 6 1 6 5 10 3 2
## [4465] 6 3 4 2 1 7 5 7 0 5 5 8 4 6 6 3 7 10 4 3 6 5 1 2
## [4489] 4 7 6 3 7 2 3 5 3 4 3 7 8 5 7 6 4 3 9 6 4 2 8 6
## [4513] 6 7 6 8 12 4 2 8 7 6 6 4 2 5 6 6 3 4 10 9 6 5 2 4
## [4537] 4 5 4 4 7 2 2 7 4 4 8 4 4 4 5 6 4 8 3 6 6 7 5 6
## [4561] 7 4 4 5 5 5 1 5 4 2 4 1 5 5 0 6 8 2 5 8 3 9 5 2
## [4585] 2 6 4 4 3 7 6 2 7 5 5 4 6 2 5 4 6 4 4 6 4 6 4 7
## [4609] 4 5 2 3 5 2 6 2 10 8 3 0 2 8 3 5 2 5 8 4 3 5 5 4
## [4633] 6 2 5 4 7 5 9 10 4 4 3 5 8 6 5 4 2 4 6 5 5 5 9 2
## [4657] 7 4 8 5 1 6 3 5 3 3 9 7 3 7 4 3 7 1 6 2 6 4 4 8
## [4681] 7 6 7 12 3 3 7 7 6 4 2 7 3 4 1 6 7 9 4 7 9 4 4 4
## [4705] 3 1 1 5 8 7 5 5 3 3 4 3 5 2 1 10 6 4 5 7 5 6 3 2
## [4729] 4 5 4 1 3 4 2 1 7 4 4 3 7 5 3 3 4 6 6 8 8 6 4 2
## [4753] 7 2 2 3 3 8 6 3 3 4 6 4 2 1 2 3 2 2 9 5 4 3 8 3
## [4777] 5 5 5 8 5 3 3 11 2 7 6 2 5 3 4 4 5 8 3 4 8 6 8 5
## [4801] 4 5 5 4 5 5 6 5 5 3 8 5 3 4 2 7 5 6 4 4 5 5 3 4
## [4825] 9 3 7 5 5 6 3 7 7 6 3 6 1 3 4 6 3 3 6 8 2 4 6 10
## [4849] 2 5 5 6 4 6 8 7 6 7 4 3 4 6 5 1 6 7 3 6 5 4 8 5
## [4873] 5 4 6 7 5 2 5 3 7 5 5 4 5 5 11 6 5 7 9 10 5 2 5 5
## [4897] 8 7 4 7 6 12 8 7 6 5 5 7 5 7 4 8 8 1 8 5 3 9 3 6
## [4921] 5 2 4 5 9 8 4 8 9 2 2 5 1 6 3 6 5 0 3 5 5 2 0 8
## [4945] 6 4 4 5 4 5 5 6 6 5 5 5 6 4 1 3 5 7 5 1 6 6 1 3
## [4969] 6 4 3 4 2 3 6 1 5 5 5 6 4 5 3 4 7 6 2 0 4 2 4 7
## [4993] 5 4 4 7 5 4 5 6hist(solicitudes, main="Distribución de 5000 solicitudes al sistema en 1 hora", col = "green")
prob_menor3 <- mean(solicitudes < 3)
prob_menor3## [1] 0.1326Interpretación: En promedio llegan 5 solicitudes por hora. Al simular los datos se observó que la mayoría de veces llegan entre 3 y 7 solicitudes, siendo poco frecuente que lleguen menos de 3. De hecho, la probabilidad de que lleguen menos de 3 solicitudes en una hora es cercana al 20%, lo que indica que solo en pocas ocasiones el sistema presenta una baja carga de trabajo.
2.Tiempos entre llegadas
El tiempo entre llegadas de solicitudes sigue una distribución Exponencial con media 12 minutos. a. Genere 5000 tiempos entre llegadas. b. Represente el histograma.
set.seed(1610)
tiempo_solicitudes<-rexp(5000,12)
hist(tiempo_solicitudes, main="Distribución del tiempo entre solicitudes con media de 12 minutos", col = "orange")
Interpretación:El tiempo entre la llegada de solicitudes es variable, pero la mayoría de veces los intervalos son cortos, cercanos a cero minutos. Sin embargo, en algunas ocasiones los intervalos pueden ser mucho más largos. Esto muestra que, en general, las solicitudes llegan de manera continua, pero no se descartan lapsos prolongados sin llegadas.
3. Duración de la atención
Cada ingeniero tarda en promedio 30 minutos en resolver un ticket, con una desviación estándar de 5 minutos. a. Simule 5000 atenciones. b. Grafique el histograma con la curva normal teórica. c. Determine la proporción de atenciones que superan los 35 minutos
set.seed(1610)
ticket<-rnorm(5000,30,5)
ticket## [1] 33.223829 35.593387 36.087595 30.369315 28.491886 32.320649 33.913056
## [8] 37.822226 22.744591 32.291824 27.541675 38.118244 23.848067 31.028738
## [15] 30.719112 35.755413 22.653131 28.059309 34.392622 34.231577 28.343546
## [22] 26.464487 27.293965 39.105628 30.744255 34.793906 28.501540 29.611494
## [29] 22.205282 21.607257 28.329318 28.959487 26.143084 29.834363 29.769907
## [36] 32.906864 33.592362 36.659112 32.684926 41.580472 26.389168 29.742648
## [43] 25.993464 26.534096 31.795976 20.934163 22.864053 26.365148 35.190730
## [50] 35.063376 30.623121 23.006057 22.044881 30.277432 30.819886 33.820599
## [57] 22.434051 35.486127 36.026096 31.293714 33.397576 28.090073 23.177126
## [64] 25.576129 31.967326 26.462771 34.528741 30.675213 32.644972 29.711681
## [71] 25.765911 26.883898 33.790606 25.517220 35.622188 32.387107 29.686121
## [78] 36.762097 30.165393 30.169529 34.371946 35.145631 31.164394 28.321431
## [85] 36.577695 26.217861 42.537748 31.634907 31.256913 29.932638 30.413859
## [92] 32.285943 28.712003 32.778162 30.174886 33.287324 31.984432 32.035304
## [99] 31.659892 31.081515 29.570989 34.956218 27.362928 20.829015 25.767042
## [106] 30.033326 34.648770 21.561178 34.443960 35.545974 30.214118 35.242159
## [113] 26.568973 24.223118 41.020211 32.076822 30.489374 33.525371 36.380696
## [120] 33.994507 18.688711 33.383400 31.166559 29.724166 29.002305 28.972146
## [127] 34.155219 24.921746 27.833136 40.123139 42.614603 27.580442 30.941319
## [134] 28.087366 32.570523 33.403922 29.895696 30.536472 28.111697 27.806365
## [141] 38.049900 30.326726 33.481740 29.612257 37.696027 24.826728 30.107128
## [148] 30.040049 18.472678 31.003989 36.797254 19.357384 27.207004 33.576585
## [155] 19.039576 26.630623 34.926109 33.304368 29.482716 24.788518 28.723573
## [162] 27.370396 31.505047 34.484809 30.331539 24.777261 30.470560 31.267835
## [169] 27.481474 31.074997 42.313065 28.536170 17.357230 25.741175 23.366338
## [176] 32.874652 27.682243 16.711670 26.103079 31.791199 28.142426 32.555247
## [183] 26.197122 30.790955 29.102646 27.740296 26.819177 31.952535 32.473190
## [190] 33.415457 30.079898 30.248182 28.761924 28.771638 25.229282 29.916031
## [197] 20.760412 22.393182 26.836372 30.937002 32.257744 32.614212 26.089652
## [204] 21.621734 39.661636 29.694386 36.259314 32.001339 22.512914 37.347888
## [211] 24.630984 34.724962 37.297397 25.614851 28.116908 34.377516 30.469827
## [218] 25.536176 32.735520 26.111056 23.938440 29.065143 24.450120 34.537561
## [225] 28.891313 30.138593 33.443583 34.276508 37.380127 32.334743 31.118625
## [232] 22.874353 22.999693 36.272209 29.848797 32.857987 34.550132 27.209034
## [239] 25.403538 29.714574 29.826380 27.494979 24.238469 35.275523 22.056325
## [246] 26.843776 27.640823 28.379871 23.425238 36.600490 30.832100 20.823075
## [253] 32.954075 29.402779 30.486213 33.113151 24.722182 32.418598 30.063740
## [260] 29.614567 25.130503 40.755853 19.657534 24.838535 26.120840 33.443799
## [267] 29.574862 35.844423 36.612641 39.610556 28.547449 27.497981 22.742456
## [274] 37.343608 27.885204 44.705295 37.541372 28.914395 22.482620 33.797564
## [281] 22.832427 20.930633 23.213717 31.489397 40.568139 37.754182 36.250028
## [288] 23.033055 38.545127 38.959471 29.300142 33.275368 37.269190 28.251593
## [295] 34.208753 33.067766 27.316333 25.831830 31.538956 38.670297 26.622986
## [302] 27.133017 31.283128 40.617361 26.619337 32.205902 22.249876 22.970126
## [309] 28.148222 32.258914 33.427734 24.285023 27.779725 24.018567 22.843297
## [316] 35.750104 37.957515 24.028605 35.649451 29.580917 34.786531 40.003163
## [323] 26.150263 26.459014 32.945562 30.956534 34.789036 23.258064 34.576711
## [330] 32.957278 30.067469 26.244540 30.918490 29.519154 29.004464 33.067499
## [337] 25.827900 25.286878 28.572394 33.564294 30.009330 19.304223 21.431039
## [344] 31.482998 33.578665 28.473691 34.139202 38.015816 31.575655 30.192793
## [351] 37.751372 33.643365 32.054635 33.736962 27.271752 24.386929 23.090532
## [358] 31.408337 29.203093 8.972081 39.181080 32.017111 33.797393 35.198505
## [365] 32.456670 31.781251 25.058147 27.596770 24.185395 23.156125 28.958357
## [372] 41.180277 17.923066 22.243675 27.083753 27.452702 34.242206 32.842042
## [379] 34.086221 22.764681 30.026094 36.528894 23.081358 30.333974 24.660965
## [386] 28.129641 35.130559 22.842635 33.782557 29.328448 24.782272 32.667667
## [393] 27.104978 33.063562 27.681890 37.869560 37.292472 28.530803 30.212270
## [400] 36.022571 20.061760 30.278783 30.849993 29.231486 27.426155 38.826967
## [407] 31.792369 24.243791 34.683848 27.643914 41.447794 34.438616 28.638116
## [414] 26.504678 31.506824 35.074853 31.383052 26.903328 39.899440 37.196778
## [421] 32.325919 39.663594 30.923561 29.518125 33.385389 33.048742 33.708210
## [428] 25.174668 29.192635 33.350145 31.497550 34.952196 34.717277 28.627229
## [435] 31.593163 33.243094 33.465731 32.200364 30.918361 30.831562 29.383227
## [442] 27.115355 31.014742 28.306581 29.280048 30.071058 18.760021 27.686905
## [449] 37.631969 22.923857 28.212707 33.651748 29.840409 27.621082 29.130957
## [456] 27.970082 22.734203 33.934477 31.708098 28.723416 39.963334 31.218567
## [463] 23.111125 32.245643 33.278208 32.268961 30.610286 26.946732 24.220796
## [470] 31.503149 32.424144 29.433233 24.671353 25.144220 37.650180 29.197940
## [477] 27.092160 29.476447 29.399493 21.292681 30.990938 29.442035 35.138974
## [484] 31.225017 31.929889 38.089175 33.239149 26.075113 23.359596 23.998525
## [491] 37.936628 28.056183 27.530544 21.446738 33.961134 29.959064 36.185111
## [498] 26.470406 32.434643 31.890302 31.194452 25.706060 27.977186 24.381713
## [505] 28.927466 31.124746 33.489934 25.727631 34.281618 29.784370 27.388569
## [512] 33.976171 34.928698 32.295909 34.273058 38.911390 31.371983 31.359716
## [519] 26.507675 26.466414 26.661886 23.177904 36.073185 41.568924 25.155895
## [526] 22.899622 37.500624 27.239374 33.328975 25.056267 33.540724 26.456052
## [533] 31.633861 19.665585 26.314948 30.412543 30.844449 29.304278 23.437373
## [540] 35.108729 27.634263 30.637098 30.401256 26.939369 21.115396 32.763359
## [547] 30.596186 28.890642 33.315631 34.270056 26.769070 29.896001 29.547866
## [554] 31.995710 31.407854 38.955441 31.444390 24.420531 25.683511 29.025748
## [561] 24.312469 31.316999 33.919706 25.726692 20.409042 24.865908 32.073134
## [568] 25.515664 22.050161 30.313691 32.283464 29.755752 33.261267 16.928773
## [575] 29.339674 40.692659 31.565548 28.130687 24.212500 29.670787 27.778868
## [582] 31.014070 29.020050 27.839257 36.009398 26.284004 28.388598 33.495969
## [589] 29.714792 24.034528 27.258021 36.041191 31.411163 34.685736 30.773669
## [596] 25.301936 28.908937 28.541604 27.407595 33.874121 31.621253 23.647375
## [603] 36.171906 24.846592 28.660439 31.061772 30.879140 34.037858 34.421899
## [610] 30.547667 30.970228 32.093014 13.564128 27.445546 31.463104 27.822873
## [617] 27.660003 29.736593 30.228618 28.644557 28.214721 27.990810 38.655237
## [624] 32.178311 21.760306 48.286627 23.061863 29.613201 34.054777 25.795855
## [631] 32.352038 30.790768 27.930944 28.062420 32.533239 32.565918 29.732140
## [638] 30.804150 42.365200 31.035991 25.482450 35.285092 33.900701 31.071687
## [645] 35.385445 30.096969 39.406679 37.038076 39.502540 23.762263 27.874393
## [652] 32.077933 20.778975 24.496952 31.345658 27.573387 37.081368 28.944420
## [659] 28.049583 32.345243 22.503058 34.975198 21.404533 28.527066 24.569837
## [666] 27.382250 27.094304 38.278407 36.537791 35.670449 30.949826 27.129608
## [673] 29.398724 28.033092 34.622684 29.616550 31.001629 32.369216 29.627711
## [680] 24.298721 39.448533 35.785758 30.887721 20.640208 20.496747 28.324434
## [687] 26.706347 30.552628 23.937406 36.857772 38.190694 27.590465 36.313245
## [694] 16.519505 25.366104 26.408587 23.830439 33.494958 26.038370 41.187702
## [701] 27.708025 26.432623 31.183330 28.574464 37.600862 33.602106 22.580628
## [708] 29.031845 36.399433 28.387637 33.614764 30.404477 27.898718 24.521334
## [715] 24.681424 28.420319 27.685017 37.142712 30.165625 25.330979 18.772712
## [722] 24.123347 37.157486 33.045749 24.504993 27.750027 19.659137 20.360445
## [729] 34.222182 21.948628 28.359675 21.704328 28.627344 34.882669 30.723672
## [736] 28.526160 40.459462 34.542802 30.481896 26.762113 34.588242 21.770195
## [743] 30.652198 34.403144 34.896577 23.156083 26.431031 44.221255 33.897075
## [750] 31.886935 37.701161 28.644169 28.872904 26.221527 31.827620 25.931137
## [757] 31.593635 26.524151 21.097554 32.934637 27.753000 26.605831 44.600746
## [764] 29.435095 17.517986 23.939009 32.749552 36.622405 30.267914 30.546299
## [771] 33.819059 26.574246 34.996557 24.682781 33.634564 17.247348 40.995894
## [778] 31.563771 28.297368 30.619023 27.182458 34.326011 23.280792 32.396930
## [785] 38.827291 30.749026 32.548142 27.360261 23.347714 28.477944 27.003243
## [792] 25.610673 40.232308 31.220843 29.514048 35.419190 36.172831 32.251029
## [799] 32.876192 27.692231 26.172592 20.100533 36.786917 29.686528 42.761111
## [806] 32.138732 33.320559 34.432554 43.545127 33.646492 29.839797 34.588201
## [813] 34.213640 22.737068 32.581876 32.331494 25.600722 30.993327 26.651593
## [820] 30.783533 30.694468 33.009955 30.222155 31.066812 23.299616 33.508582
## [827] 25.849230 19.145952 32.518510 19.881346 30.241038 31.531674 28.864336
## [834] 27.484934 35.311029 27.863701 36.229426 33.487007 38.715763 21.966164
## [841] 30.574844 27.300965 29.640985 28.092277 42.012288 29.507263 27.578510
## [848] 37.458746 26.084204 25.063862 26.768544 23.085194 34.171146 22.723210
## [855] 24.038604 35.970749 29.750605 31.955467 29.504925 27.033306 27.812753
## [862] 21.611862 18.260539 37.069547 26.991472 27.475374 25.553366 27.045863
## [869] 35.765384 24.523335 27.522806 37.777926 19.803522 35.986276 23.757652
## [876] 31.794569 26.432269 26.467178 37.552691 31.201638 31.846919 33.628149
## [883] 32.064426 27.135709 22.715385 37.226732 23.442638 31.590534 29.379328
## [890] 34.997551 31.106165 29.164167 28.560687 29.997035 26.464469 33.254444
## [897] 26.093356 39.372654 25.509018 32.916981 34.163681 34.894261 35.124392
## [904] 35.399196 29.054807 22.942471 22.793408 25.041974 34.013808 40.233384
## [911] 35.085545 23.824453 22.284699 28.310973 20.122697 37.787711 22.997246
## [918] 22.694380 27.090292 21.688862 25.072115 28.517091 22.906185 24.767891
## [925] 31.192464 29.212943 29.871088 27.328704 29.183452 29.202627 23.688300
## [932] 33.992387 29.935677 32.582864 28.311465 31.766164 30.751005 27.281448
## [939] 36.316755 29.682020 37.655555 26.580479 32.497309 25.021888 30.482982
## [946] 23.889716 29.120437 25.723865 36.859033 33.320478 34.038770 29.269713
## [953] 26.823336 35.324282 30.484885 26.136913 23.814337 30.072924 35.266598
## [960] 12.946208 22.611717 32.132999 26.154314 36.193040 34.966244 38.269486
## [967] 29.223233 26.136335 38.391001 40.326874 22.161601 29.502480 25.822080
## [974] 20.640278 34.986680 28.142665 33.982097 34.419770 30.892056 37.998704
## [981] 19.932648 33.207406 31.332951 30.102189 36.458952 37.630546 31.135698
## [988] 17.253266 35.764988 30.672963 23.021559 26.770624 33.689048 28.580850
## [995] 35.700785 25.374324 23.021697 29.088172 27.726147 30.737363 34.338585
## [1002] 23.778033 22.377644 31.041030 33.835973 29.563541 38.517101 29.196512
## [1009] 33.010908 40.531470 26.942459 21.978721 27.014099 32.475311 32.631585
## [1016] 34.733715 28.279472 32.191100 27.251451 42.699857 27.460118 29.140610
## [1023] 22.155190 32.239067 22.326527 24.579991 25.577059 23.661834 25.422275
## [1030] 29.278127 28.739654 25.483340 35.537142 32.445598 24.481120 33.816459
## [1037] 29.429001 36.491807 36.091426 13.256572 30.833429 34.512139 27.885534
## [1044] 29.470739 36.788557 39.031335 28.457128 31.977602 31.831884 28.757487
## [1051] 27.411107 32.832204 31.118191 28.862096 27.404729 37.376140 38.503503
## [1058] 30.851362 30.667456 37.332098 35.697242 33.931331 36.953236 31.146922
## [1065] 22.613612 34.394858 38.963752 27.397052 27.089754 37.061256 28.334641
## [1072] 23.001645 22.701495 34.939393 33.920744 32.889573 25.113872 27.027885
## [1079] 29.327996 31.905332 30.709197 23.100293 33.183576 32.876620 28.821975
## [1086] 33.429313 26.979883 51.041945 31.707529 36.425784 30.325060 33.873665
## [1093] 32.665165 30.219466 29.604032 35.743148 30.500280 28.619716 30.146522
## [1100] 33.915212 19.609729 31.523847 27.836459 23.128083 33.046073 37.151033
## [1107] 32.870577 27.314131 30.532402 43.529889 34.245416 35.335045 29.392215
## [1114] 26.643495 29.488107 34.164644 29.445377 25.370401 31.117449 35.291244
## [1121] 33.934870 27.762975 32.475053 23.592087 35.007663 24.160565 30.373617
## [1128] 21.947452 31.653001 26.305664 31.242107 35.402470 32.487827 42.690422
## [1135] 32.976469 24.722835 32.811743 30.732866 29.465726 34.262520 38.583865
## [1142] 20.376657 33.398902 26.847259 30.100892 34.867955 32.488966 25.036730
## [1149] 28.576208 29.623999 28.183773 32.048584 35.125131 29.699388 29.013374
## [1156] 36.952891 22.921192 23.611018 37.246649 31.032753 30.490948 34.826379
## [1163] 31.651216 32.489285 40.358460 33.488281 24.855146 29.179294 25.361555
## [1170] 32.904714 35.192001 21.579422 28.318740 26.282919 32.838092 28.458034
## [1177] 32.923202 33.819271 27.826316 37.872478 31.632083 27.675730 33.023708
## [1184] 34.238480 36.712690 33.947420 28.542641 26.561747 22.596259 21.939475
## [1191] 27.693080 26.853002 33.179334 28.988641 39.337188 31.097181 25.402355
## [1198] 29.015366 22.014256 28.599318 22.993528 37.209477 28.557391 24.468585
## [1205] 29.543818 25.395144 32.228025 27.141090 27.353488 35.698497 36.530748
## [1212] 30.458689 26.751652 24.939037 28.884728 34.527583 30.470237 29.207824
## [1219] 33.465657 31.721190 31.003473 29.620058 22.064606 29.876669 31.946926
## [1226] 35.023117 32.654904 29.679247 19.629247 25.916592 29.707725 28.092214
## [1233] 22.064785 31.627894 36.538404 28.838430 25.799147 24.886973 35.239531
## [1240] 38.369498 23.780822 30.633556 22.596756 35.591351 27.898506 32.366585
## [1247] 28.103882 22.614011 28.715995 31.046612 30.789173 32.767624 29.457873
## [1254] 33.865510 20.712635 32.429507 21.970147 28.891427 28.790307 26.609037
## [1261] 17.929532 15.795898 26.870162 36.325677 26.265117 28.324731 30.689976
## [1268] 28.108841 35.137883 35.077575 23.420424 23.338538 28.569207 27.318905
## [1275] 33.842662 25.399543 36.251643 28.948447 28.981685 35.114779 29.041401
## [1282] 37.682517 28.373619 32.308122 33.729053 35.364475 23.700024 27.226089
## [1289] 26.439019 29.253494 31.743978 26.148785 30.242202 22.635668 22.991096
## [1296] 34.707599 26.559248 38.590010 36.850851 32.355965 29.210322 32.926880
## [1303] 35.216355 21.432144 23.527740 29.994424 31.830662 20.620943 28.508221
## [1310] 31.851883 35.002207 31.193462 35.743639 33.018995 16.507416 27.083022
## [1317] 34.620362 28.848320 40.251254 31.314601 43.592848 27.244092 32.427712
## [1324] 37.773353 36.996832 38.500568 31.937298 28.771902 31.255598 25.453629
## [1331] 31.817504 26.193709 23.797871 35.186158 26.236266 30.067553 35.872897
## [1338] 24.302300 27.843687 38.277046 17.907455 32.945724 32.210745 38.710777
## [1345] 34.622738 28.304333 35.728022 31.198381 34.585743 25.032408 23.534773
## [1352] 29.164235 28.170507 23.841291 28.061073 28.744526 37.935606 31.842995
## [1359] 31.018522 27.594224 23.592152 29.260733 41.461366 23.988090 33.051644
## [1366] 32.793809 31.470067 32.002832 33.550241 25.084029 31.942526 33.091783
## [1373] 31.181039 31.382040 22.734885 28.885199 23.101360 25.436148 25.980292
## [1380] 32.745728 31.748234 28.765431 33.870645 40.288399 38.267647 32.427628
## [1387] 32.242790 29.060375 34.354790 28.901883 27.091938 30.825337 29.244117
## [1394] 18.292116 40.358865 21.115206 36.404989 30.092140 34.666919 29.437996
## [1401] 32.218945 29.474068 21.416780 27.039760 28.639574 25.989394 23.265669
## [1408] 32.146774 28.652783 35.600902 33.754484 19.726957 22.909551 32.981783
## [1415] 31.705581 25.724887 40.301874 33.664277 20.499674 29.152076 26.200559
## [1422] 28.958339 25.170059 30.734875 34.496490 33.192755 30.901734 28.126059
## [1429] 40.884131 32.213983 34.558691 32.611431 27.485524 28.409916 37.041677
## [1436] 31.566662 36.896966 38.059346 30.339970 33.692240 33.747178 26.491213
## [1443] 30.875293 24.148434 16.759205 32.443838 27.865538 23.117440 27.632622
## [1450] 36.523738 35.013875 27.643145 35.452167 24.287077 23.505378 21.921459
## [1457] 21.270627 28.095369 33.242961 42.432390 23.129090 30.497637 26.359702
## [1464] 31.063262 28.374767 39.630010 29.116983 33.626988 22.600418 29.516507
## [1471] 37.237576 32.160693 20.272506 26.409353 23.641687 34.840801 26.519490
## [1478] 18.898632 33.312825 29.899794 38.258330 35.547559 28.165955 21.327361
## [1485] 28.564224 24.332536 33.463085 33.294371 33.698993 28.018451 33.310552
## [1492] 23.348402 24.604071 25.182485 20.821050 29.352383 32.221638 30.197788
## [1499] 37.558497 21.999941 30.099763 36.210105 24.748288 21.543081 32.425229
## [1506] 33.357299 34.958439 29.201578 26.213578 34.149809 34.694345 27.206684
## [1513] 36.496083 22.071321 26.379649 26.457042 36.470630 32.787198 31.095886
## [1520] 26.803046 31.826650 31.621784 25.473208 33.486086 26.547672 33.757191
## [1527] 36.587196 29.553529 36.263370 27.535708 30.073152 34.596790 32.184775
## [1534] 28.685651 31.999436 33.487699 32.294961 29.961855 21.658433 27.215288
## [1541] 33.972807 33.317606 21.541998 30.456137 26.760685 24.296957 39.794935
## [1548] 23.332765 21.967795 25.974409 25.805535 39.559786 35.835789 31.957631
## [1555] 39.154461 23.618812 21.018833 25.597928 31.875911 31.770741 36.373629
## [1562] 34.802728 38.738771 34.027821 27.605749 26.919895 30.136019 29.688413
## [1569] 33.318196 25.040941 30.967783 27.908694 41.022467 30.507885 30.449675
## [1576] 36.230949 23.840824 23.805554 41.077740 31.169768 37.580960 33.217034
## [1583] 35.871383 37.741832 19.663864 22.957467 27.909607 37.294591 50.144177
## [1590] 29.428267 20.009202 30.831971 39.125254 25.825549 25.769489 32.189491
## [1597] 31.170647 30.334184 27.741245 27.915894 27.138342 24.759559 26.540740
## [1604] 23.019378 28.033159 29.935165 28.759074 30.094665 22.646019 31.870553
## [1611] 27.057837 19.611623 32.914694 29.332879 32.200368 30.835036 30.595841
## [1618] 27.747685 30.208073 36.121704 30.445515 27.963911 30.516491 30.178144
## [1625] 29.938364 31.726927 23.991246 25.581461 24.903989 33.671555 31.077769
## [1632] 28.506943 23.594019 38.308593 30.467718 34.482645 32.916895 25.898170
## [1639] 27.840415 23.439353 31.751768 23.249362 29.919314 31.260765 26.183932
## [1646] 22.854984 16.742627 27.013967 35.715999 33.380640 27.463369 36.723033
## [1653] 30.306953 27.897743 24.511441 34.519085 34.726703 35.381457 22.220882
## [1660] 21.447420 28.506711 25.078331 30.124360 28.475208 36.753568 32.730448
## [1667] 27.822842 30.999512 36.646599 24.419872 29.466128 26.830450 27.597345
## [1674] 25.714531 27.084705 38.571361 35.903892 26.850008 33.849748 28.814863
## [1681] 12.124064 24.113087 40.092047 25.868061 32.917861 20.868740 20.632975
## [1688] 25.613220 24.407716 35.398632 34.096879 29.354654 28.186354 30.727209
## [1695] 21.340497 18.675437 19.488454 32.265295 39.764397 28.574874 31.876573
## [1702] 31.627651 23.959587 30.535553 23.913508 28.315046 31.141509 28.277781
## [1709] 33.716572 24.100365 29.385849 27.387179 29.280357 27.042756 26.278915
## [1716] 25.303787 30.437024 26.208834 23.902707 26.198282 33.173126 32.860018
## [1723] 21.208488 30.775338 36.613516 33.052335 32.031553 37.352474 34.891810
## [1730] 30.350975 26.683582 25.419937 35.813325 25.222389 29.178367 24.585883
## [1737] 35.606589 34.873832 38.398583 25.392150 29.127263 34.035942 33.879382
## [1744] 27.813978 30.762296 31.756708 27.110507 32.693207 20.354498 27.913806
## [1751] 30.437978 31.195118 25.460348 36.502126 33.166611 34.099536 36.703641
## [1758] 26.343863 29.320302 30.479908 29.823845 37.369662 31.132853 27.689338
## [1765] 34.530761 27.975516 26.168377 36.598719 32.738688 39.356869 31.274052
## [1772] 34.113563 17.631902 39.559538 27.204185 32.802887 34.811519 24.156604
## [1779] 30.677448 30.198510 44.124123 21.823248 26.133820 36.161610 29.610385
## [1786] 24.407745 37.077439 40.878419 29.673756 28.032819 28.464823 39.899949
## [1793] 32.237976 25.943932 30.671465 32.270939 23.730257 28.489965 28.676259
## [1800] 29.224477 32.178150 33.799405 33.605976 39.084539 30.149504 15.052095
## [1807] 34.854529 30.259463 37.271853 38.404835 35.665990 30.922633 25.202528
## [1814] 34.536776 26.580169 33.502009 37.775740 29.382564 36.419649 24.362321
## [1821] 32.078966 38.006289 32.423455 34.301671 25.561426 36.893876 37.313517
## [1828] 32.220655 24.691529 29.773595 25.903660 23.175591 27.946359 17.881987
## [1835] 27.048300 26.380952 27.654747 26.078532 24.179478 33.171613 33.902149
## [1842] 24.780416 28.398968 37.522652 28.991692 31.557068 27.855394 34.009103
## [1849] 32.874318 38.813877 29.208276 23.663568 38.599447 36.108933 37.620671
## [1856] 18.635810 26.799100 32.339221 27.541246 39.072865 18.963047 30.003163
## [1863] 29.601575 37.530043 31.850082 32.581703 38.402134 32.125853 29.739690
## [1870] 24.086977 32.325822 26.885827 27.461511 39.443952 30.464733 30.802728
## [1877] 30.969886 22.081604 30.731894 27.400096 25.999220 20.820164 31.026390
## [1884] 36.355472 35.637165 34.825642 27.130431 29.381087 30.333514 30.172089
## [1891] 35.532938 28.719655 30.945411 33.396312 26.802404 44.577479 31.127038
## [1898] 34.966621 29.377162 35.777627 30.189802 32.060193 26.592936 33.744074
## [1905] 33.725392 25.691072 35.713630 24.208165 34.289957 28.082415 30.216418
## [1912] 28.204557 39.932406 26.612516 31.091360 33.365220 25.344909 20.751400
## [1919] 37.443222 30.407858 30.055993 38.624013 23.921782 30.542624 26.754480
## [1926] 25.665824 35.298384 25.132956 25.948604 33.097993 28.756852 34.634779
## [1933] 30.411215 38.823990 39.770460 23.391951 33.716031 27.906494 37.603211
## [1940] 28.293057 30.404043 28.930059 41.239555 32.464660 26.679686 30.495392
## [1947] 19.826210 31.612341 31.530916 31.147300 31.412724 25.318868 31.947507
## [1954] 21.967521 30.203584 23.061368 20.162087 30.317808 35.492116 33.872136
## [1961] 28.497063 36.667060 25.157714 22.097974 32.385110 30.929964 27.330106
## [1968] 32.497310 17.523372 27.604113 39.429941 29.065007 28.188857 38.262785
## [1975] 29.529540 21.358442 23.121558 34.251849 30.672995 35.083480 29.746906
## [1982] 30.020164 33.895771 23.561332 28.097580 30.505662 36.501061 19.064548
## [1989] 26.328758 26.718569 47.298849 33.810728 23.468947 24.319568 31.258322
## [1996] 29.443101 39.176428 29.827774 28.144354 33.542715 27.193555 45.073456
## [2003] 37.410238 31.511845 25.928525 27.205436 28.205927 35.964074 25.254474
## [2010] 32.294141 30.773867 29.292400 37.199398 17.042525 34.291893 23.981636
## [2017] 28.105606 28.596983 33.276638 29.254615 31.464725 34.749399 23.098590
## [2024] 30.860434 31.315894 33.257150 34.955536 28.201587 22.304082 28.680846
## [2031] 24.270974 27.495649 29.330554 28.614216 32.204037 29.302315 32.649887
## [2038] 26.098735 38.962886 36.247371 33.583296 29.899635 16.477255 28.493791
## [2045] 40.793188 27.933806 32.327752 32.532187 25.948341 26.005834 38.225848
## [2052] 31.129021 27.197615 34.418999 26.028913 27.154469 30.649692 22.075621
## [2059] 24.354281 28.144127 42.188407 27.547296 27.959545 32.005508 30.046186
## [2066] 29.725483 36.690257 29.330390 38.260131 24.013826 29.065498 22.700696
## [2073] 26.486841 30.973967 26.357067 35.531349 30.022250 32.956818 19.483175
## [2080] 28.467794 25.081839 20.153145 35.974213 23.790455 27.301359 28.200862
## [2087] 28.031252 26.778960 35.225935 32.577971 27.280993 30.749690 33.844569
## [2094] 31.932695 35.233133 34.957324 24.365043 29.364450 28.493134 24.422678
## [2101] 29.271954 25.342813 34.247895 25.725027 20.547569 33.691501 33.562023
## [2108] 28.901083 32.228654 23.129979 33.322265 28.234562 28.888184 36.700462
## [2115] 28.092671 33.982976 36.569994 30.347797 20.931359 29.382407 32.901053
## [2122] 23.907251 32.336995 28.954913 31.809987 35.381405 26.959960 26.670411
## [2129] 27.484220 34.941904 24.717018 34.352619 38.221826 27.196199 33.866552
## [2136] 38.223987 28.461784 27.052511 35.567091 31.609947 34.708026 27.164956
## [2143] 24.441300 37.097764 29.622195 37.017021 31.273456 29.110301 43.990080
## [2150] 34.413218 27.918231 35.561743 17.824278 31.534813 31.274624 28.039335
## [2157] 25.334438 32.359787 15.567224 29.760980 27.180132 24.329807 28.722615
## [2164] 39.349959 23.370799 30.538296 28.760458 35.852391 25.175100 24.951578
## [2171] 24.254137 27.473474 22.109307 22.783295 22.531115 31.060681 26.068942
## [2178] 21.799160 32.381091 26.546792 33.706875 26.565864 27.751258 31.231743
## [2185] 34.569172 22.308491 24.327624 37.055628 28.538470 30.469283 36.254564
## [2192] 28.695901 24.586763 37.383486 24.510290 33.600168 34.948153 32.391791
## [2199] 31.533982 28.003959 32.690142 27.899788 31.413452 25.658697 30.192210
## [2206] 37.766178 30.051589 24.101553 35.311312 21.706505 26.084396 28.326741
## [2213] 33.011314 22.734250 28.296062 20.352771 30.893537 36.180202 35.062242
## [2220] 26.574932 29.240734 23.150045 32.853847 21.317835 33.417271 36.710990
## [2227] 31.982839 26.685961 35.448730 20.716779 31.205445 25.594364 32.675495
## [2234] 28.429493 19.643859 31.249157 15.643189 29.812343 28.799038 31.564855
## [2241] 34.302485 27.352450 31.619624 20.237000 28.547674 32.323718 34.723629
## [2248] 24.855669 26.239729 25.257287 36.492825 33.993694 27.837036 38.179860
## [2255] 28.371682 36.986549 33.210184 31.498462 43.133259 23.951443 35.436326
## [2262] 33.286391 23.124821 33.364421 26.520786 39.991136 33.484280 21.414148
## [2269] 28.435516 28.664566 34.310506 23.707654 27.766244 36.820065 27.290230
## [2276] 31.301087 28.674274 25.647634 32.887304 31.279436 34.752490 28.945351
## [2283] 29.517009 19.398271 27.169910 29.026304 29.520787 17.629185 36.502913
## [2290] 29.621341 26.682275 31.041979 22.305805 27.494981 25.698376 31.775378
## [2297] 35.039084 30.297344 33.326486 30.322932 32.074463 27.291029 27.726496
## [2304] 28.226599 27.974171 23.334774 30.455456 32.620896 39.748377 26.689261
## [2311] 22.830385 25.288043 23.349591 36.081148 26.666035 30.142316 32.089690
## [2318] 30.954860 34.101505 38.999822 28.941042 25.614491 35.801271 30.056498
## [2325] 23.983739 33.497367 30.397901 38.057877 34.730086 37.381065 18.566574
## [2332] 25.719267 24.945457 39.235961 24.763501 28.605243 33.693971 32.399889
## [2339] 32.277432 29.107367 35.497023 34.157425 26.166250 33.702660 31.600285
## [2346] 22.497707 25.523521 20.300055 34.860331 29.118223 37.506386 28.848724
## [2353] 24.918728 19.053211 35.691251 30.101333 24.487735 27.789322 29.305352
## [2360] 20.125336 32.170078 30.238319 30.869546 25.433937 29.016773 28.779697
## [2367] 24.874264 22.434171 34.559275 28.450291 34.312111 25.964452 27.533373
## [2374] 31.718696 35.968214 29.133289 34.608342 23.670002 26.206859 32.337095
## [2381] 24.305686 32.075323 23.822625 21.618593 23.377565 38.181374 28.707494
## [2388] 37.064877 29.262561 30.185608 31.252984 26.824038 21.657267 32.262698
## [2395] 29.315111 27.161399 30.410145 26.213094 35.826552 37.227670 27.857654
## [2402] 30.064120 29.709761 32.328752 31.301073 36.442123 26.265939 23.402519
## [2409] 29.408014 28.537166 31.361799 26.223856 38.380080 34.963152 29.670161
## [2416] 26.760660 33.781937 25.964729 20.101893 29.197463 26.828584 33.264500
## [2423] 22.696001 32.272831 24.189151 31.169685 28.261329 36.447627 32.053731
## [2430] 27.518509 29.073903 30.359166 32.527166 25.586250 30.988119 36.053270
## [2437] 29.942109 31.567143 30.586259 30.852942 33.654809 29.874292 30.159485
## [2444] 41.903233 30.670865 38.098798 30.744601 30.589841 36.072640 27.800528
## [2451] 31.802539 36.693433 31.578894 31.079580 29.816768 28.727815 36.737131
## [2458] 35.981593 26.089107 26.478286 29.270860 28.293789 37.646556 27.132280
## [2465] 38.054951 21.309674 20.669101 25.702111 30.018673 26.313372 31.031488
## [2472] 16.764731 32.451423 27.895677 28.280611 29.969560 33.451249 30.952824
## [2479] 31.575654 18.252527 29.777450 30.153317 32.976584 20.040224 32.295858
## [2486] 25.591963 22.105823 31.496818 30.565169 31.109140 28.395170 25.440830
## [2493] 35.455046 24.128067 28.076275 28.994719 30.394417 27.228826 30.127721
## [2500] 30.916528 29.518936 32.197347 34.050911 38.519869 28.033192 24.960801
## [2507] 36.594947 27.805356 28.397488 33.615756 28.380097 28.123429 19.130063
## [2514] 31.101703 28.914363 29.218312 14.317114 38.333380 27.106457 36.090465
## [2521] 25.407946 29.032836 30.559763 30.602874 36.149523 33.549764 31.224577
## [2528] 27.527229 22.266295 33.748506 20.017933 29.287607 38.774546 35.882335
## [2535] 34.210351 31.071047 30.776764 27.655018 28.340735 29.913584 36.974721
## [2542] 31.133990 34.893147 30.375752 20.214292 25.005787 23.685321 22.445568
## [2549] 28.556277 24.929836 24.512927 31.673115 17.621796 31.276893 30.686638
## [2556] 34.712706 29.621089 22.205667 30.000481 24.779610 37.742688 24.606957
## [2563] 23.767959 28.233155 22.439449 27.888638 25.922448 34.835266 31.782659
## [2570] 34.782631 28.108104 34.262307 30.530019 28.522981 34.604307 29.549680
## [2577] 33.474135 29.206805 31.749908 34.147448 42.152718 34.066602 20.088808
## [2584] 30.805874 29.817886 36.181302 35.002499 29.768171 30.377255 35.565390
## [2591] 32.763839 26.450068 37.353204 29.406328 25.777587 36.336796 32.103125
## [2598] 33.752758 23.056173 32.564803 29.300198 27.285717 25.484952 26.350817
## [2605] 28.220109 27.863533 30.376780 29.179242 22.541636 31.885782 35.404368
## [2612] 23.382603 26.830252 33.976084 26.088188 25.124693 31.903203 34.621504
## [2619] 34.131903 25.184578 25.406498 27.246583 23.698251 37.239488 22.005136
## [2626] 27.704386 32.574414 40.666344 26.617893 25.831599 21.326958 25.284218
## [2633] 24.743070 23.540651 26.153186 29.323075 34.327189 33.002110 36.073141
## [2640] 30.867286 29.657468 23.417481 29.651419 21.721625 33.186011 32.328110
## [2647] 32.700534 21.479761 33.094653 33.635367 27.393347 26.208978 44.486490
## [2654] 33.780173 32.862295 32.136910 26.228557 28.909306 25.290702 32.215048
## [2661] 25.345843 17.214717 30.653934 28.594148 31.490605 25.461130 32.130846
## [2668] 30.764118 24.451509 29.763003 30.746614 28.536004 21.546901 28.165605
## [2675] 31.459573 33.114321 26.560260 29.640586 24.090505 26.255877 24.183797
## [2682] 26.408121 28.407386 36.634328 35.591278 24.433918 27.494744 34.784758
## [2689] 28.534317 30.739142 32.941078 30.035257 32.949540 18.593486 33.945658
## [2696] 36.362255 32.299976 31.224991 32.245219 28.408486 25.931326 37.724131
## [2703] 37.563207 19.732910 32.927471 28.347609 28.112980 27.330312 28.333890
## [2710] 37.319228 28.796570 31.339642 34.876124 24.070115 30.647895 31.732951
## [2717] 21.684939 27.928337 20.904222 23.644024 30.204048 25.067070 31.212923
## [2724] 30.556999 27.708350 29.834923 29.833776 24.338817 27.640155 26.866291
## [2731] 25.724294 31.442169 42.021841 34.407010 24.103956 32.274563 28.927638
## [2738] 27.604794 33.351249 27.549284 29.482045 24.447454 26.884847 33.364558
## [2745] 24.710434 33.099133 23.694021 34.565697 32.789857 27.704615 30.846560
## [2752] 34.491916 39.871118 41.175430 35.451313 39.309409 32.888372 37.498777
## [2759] 32.551006 34.177847 28.811992 38.700387 45.911700 31.302721 34.772533
## [2766] 31.258519 28.680055 34.724915 22.488612 25.788595 18.585880 27.010787
## [2773] 39.353375 28.099963 36.307119 30.904613 32.803607 34.787149 26.165102
## [2780] 27.209539 29.612155 29.030482 33.151850 27.014237 37.339514 25.887869
## [2787] 31.126197 23.166749 34.154291 32.785562 30.954983 37.199862 31.265472
## [2794] 26.805660 38.645918 30.001635 35.351437 32.275306 17.561527 27.586594
## [2801] 26.736698 30.774871 28.516223 37.883708 38.402201 20.234540 33.169345
## [2808] 30.843625 33.143406 35.362804 36.649200 24.837453 29.613578 26.589447
## [2815] 23.539010 34.237738 22.271317 23.820248 27.328786 33.290365 31.145361
## [2822] 32.558344 22.029265 33.637511 28.975519 19.457441 29.945631 30.868546
## [2829] 32.116590 25.031716 29.221534 26.452274 23.418317 34.174246 35.400942
## [2836] 37.652344 30.895881 32.441938 27.808856 38.375566 33.411005 37.148411
## [2843] 43.744394 25.366608 34.404515 28.411310 32.414641 32.500091 29.010235
## [2850] 33.052153 19.880062 30.852572 35.113599 27.413267 34.677863 29.141019
## [2857] 33.540358 26.424582 24.536303 27.430677 33.515853 32.869715 31.622860
## [2864] 27.075646 30.294104 24.995210 36.532405 30.542925 33.674598 26.073021
## [2871] 37.237829 43.248324 18.249828 36.025875 28.136494 30.634071 19.697880
## [2878] 28.656147 27.564472 21.764558 33.751055 26.142949 33.759747 33.007837
## [2885] 32.819898 28.777042 18.354539 27.864704 32.877013 25.340197 31.508836
## [2892] 37.690853 34.179031 23.352671 32.275981 33.791063 23.016729 35.138302
## [2899] 39.765763 30.211102 30.947434 25.217330 30.604616 31.641896 31.608424
## [2906] 25.730290 34.611409 26.447517 35.335640 29.231044 29.819143 23.122123
## [2913] 33.421219 34.284078 36.350760 33.377010 27.126774 34.306923 33.793353
## [2920] 34.077850 29.596793 29.700165 28.173973 28.935790 23.101512 32.022030
## [2927] 29.611148 36.213195 29.426902 30.192118 31.796003 22.447840 30.214299
## [2934] 35.737560 35.908350 25.699909 37.877215 31.552649 30.695159 38.189588
## [2941] 22.290742 33.077153 29.802357 34.779817 31.667036 33.456788 30.301085
## [2948] 29.199781 24.868804 23.979158 30.114873 26.068788 22.654943 29.997915
## [2955] 29.192719 29.645749 26.310316 16.513938 23.606815 34.856823 27.095063
## [2962] 30.592826 27.386393 23.599730 35.150604 27.505913 30.213573 34.446166
## [2969] 29.114126 28.002161 29.547476 30.117709 22.368678 30.579818 29.633630
## [2976] 31.064005 27.934498 24.954523 22.008478 26.264077 28.981762 26.467806
## [2983] 28.383165 16.943475 22.748566 27.055256 27.432411 35.529976 39.955085
## [2990] 30.633124 28.233979 21.924169 22.636061 30.524140 23.389690 31.690827
## [2997] 30.003183 30.500032 23.072997 25.739455 28.340561 25.995861 29.348620
## [3004] 23.120643 35.999163 34.369356 40.630003 34.281112 21.361444 25.872549
## [3011] 23.160478 21.211635 32.234093 33.578585 27.475889 29.304739 31.330739
## [3018] 32.454935 24.809291 30.369617 24.597375 30.972154 23.510923 19.581356
## [3025] 28.614930 29.048091 29.708630 26.593541 35.516748 27.065971 22.982634
## [3032] 24.416440 31.995490 32.174055 24.651898 28.429640 30.160776 30.136708
## [3039] 26.365901 33.114047 41.833793 40.881309 45.057171 39.241195 33.365785
## [3046] 29.745731 21.356873 33.418337 32.642783 25.204013 24.725393 32.744257
## [3053] 25.220420 30.563516 34.548535 27.081042 32.711991 30.386621 30.771337
## [3060] 32.764185 32.725025 29.311341 30.260694 42.470152 40.382931 26.531235
## [3067] 27.943136 34.930652 25.054984 32.625434 24.052691 34.731471 31.683564
## [3074] 32.140308 31.009871 34.780689 29.178338 32.327558 28.403642 32.311728
## [3081] 32.251961 29.435287 30.080381 30.295613 27.673141 23.804743 29.315422
## [3088] 26.040517 31.836454 30.236226 26.733472 23.373179 30.327623 34.670814
## [3095] 22.548694 22.337892 34.489303 18.849589 32.580322 25.716419 28.300962
## [3102] 28.871892 33.102148 34.692526 28.329120 24.877657 29.038973 26.430646
## [3109] 24.658637 28.837318 25.697567 28.957963 35.437643 19.927105 31.366084
## [3116] 30.057189 26.327414 32.528206 32.296017 30.539636 25.255109 33.095379
## [3123] 30.498996 25.403151 20.922790 27.924175 26.521412 34.976539 32.666659
## [3130] 26.999453 24.462903 22.413836 37.427216 27.436479 31.960980 35.537506
## [3137] 25.569586 35.096248 35.693209 34.736051 30.396969 39.793890 36.600140
## [3144] 29.356531 25.081679 31.037358 37.267411 21.221348 25.748535 30.079154
## [3151] 29.952169 34.240469 30.813059 36.407452 35.812890 32.690154 26.301232
## [3158] 31.729403 22.265663 27.870460 27.844514 32.171641 31.944891 29.763517
## [3165] 33.720107 25.933113 30.259758 33.124154 26.244726 26.095370 30.739271
## [3172] 38.115880 38.173115 25.202221 28.325196 26.931460 27.678945 22.426842
## [3179] 31.639831 31.990682 30.942088 26.142541 30.716741 34.225540 23.641706
## [3186] 43.925504 24.873918 29.428103 27.388965 28.946015 16.663730 31.071144
## [3193] 30.982232 27.881809 27.821897 35.723832 29.281646 28.326426 30.876616
## [3200] 26.740216 31.668471 30.861024 35.695315 33.026046 24.698263 25.754945
## [3207] 25.338338 29.072121 28.516604 29.323495 29.347814 26.411682 30.561877
## [3214] 30.564003 33.132924 27.275542 35.899132 29.156140 38.972240 39.955046
## [3221] 32.071970 27.972369 32.828775 24.412256 32.543790 22.246398 15.739447
## [3228] 29.758660 26.440780 38.447197 24.593602 28.714818 38.895984 36.734416
## [3235] 31.586006 27.879498 13.252905 32.837255 31.103171 32.642219 36.313382
## [3242] 27.134177 26.068988 28.589344 31.459915 27.818129 17.063107 24.676222
## [3249] 33.821170 28.631970 26.631517 31.349394 21.274226 27.356823 40.191017
## [3256] 17.735631 29.042541 25.852471 41.508843 25.247229 27.032096 27.659872
## [3263] 25.327722 21.730143 33.905522 32.700045 33.247666 34.817607 35.845227
## [3270] 27.783496 27.642549 35.179380 26.934960 20.938262 26.423966 32.825641
## [3277] 39.119754 39.233962 24.449900 26.721354 22.113889 34.790105 39.716027
## [3284] 33.273849 40.062592 30.426803 21.066339 33.826813 27.166899 21.718193
## [3291] 39.607313 32.258907 27.649255 37.002500 30.199959 35.602417 30.319387
## [3298] 31.476687 29.650695 29.194635 28.751921 33.228167 28.392186 29.892439
## [3305] 27.131073 25.200626 29.329682 43.491294 32.783552 25.876917 36.563270
## [3312] 22.407727 30.885610 26.338381 32.851016 25.074220 27.398533 29.743269
## [3319] 24.116158 36.511455 40.264894 25.431057 30.335842 21.028871 30.017895
## [3326] 30.667688 28.652079 35.626595 21.767222 33.281276 30.559956 33.444023
## [3333] 24.446457 28.368493 27.202447 30.661407 39.708102 34.570348 31.085028
## [3340] 33.562753 37.014901 35.282398 33.285483 32.852362 33.596470 38.805059
## [3347] 30.780577 33.341368 30.325070 28.091586 21.583136 29.365342 23.617828
## [3354] 25.591759 25.541196 32.625068 25.965718 30.726243 29.953248 34.432365
## [3361] 27.012409 18.794922 31.474516 23.691076 27.404604 25.923856 27.383544
## [3368] 30.876861 25.997655 34.160650 22.049635 32.023631 30.407507 33.726611
## [3375] 29.223823 29.535889 27.188813 30.188467 28.936892 30.510863 27.307938
## [3382] 29.182484 21.119716 23.336896 25.845245 31.969419 29.673258 27.851473
## [3389] 31.177268 21.993644 23.570226 30.825562 36.065407 35.295771 27.642327
## [3396] 29.662627 30.190681 36.553310 38.043447 29.166738 28.990953 24.933837
## [3403] 35.939245 28.459569 38.566938 29.115786 23.165651 34.559988 23.176776
## [3410] 36.439013 28.839257 44.635393 29.872728 32.235349 33.121316 35.221471
## [3417] 25.572704 31.004431 16.148055 28.646056 21.856751 29.834501 24.538753
## [3424] 24.537480 31.462219 32.499591 25.441783 30.117290 29.112205 36.795870
## [3431] 37.002471 29.389497 24.667543 40.668273 33.098209 27.676441 31.050953
## [3438] 26.880778 30.046743 32.137336 33.499477 20.724091 30.199426 23.975431
## [3445] 20.232740 36.387851 30.726716 34.815928 30.487237 35.246447 34.698514
## [3452] 28.443851 27.980198 17.787248 24.193978 27.484675 29.841021 32.781176
## [3459] 24.007291 24.904619 22.295383 27.951424 31.770623 35.623346 22.895286
## [3466] 28.371941 34.001247 21.351969 29.623946 33.208332 34.538925 28.535651
## [3473] 30.597690 33.345549 33.275293 28.284216 27.964812 33.215370 34.508085
## [3480] 22.029099 19.062001 29.655850 34.197668 22.041361 32.930824 33.157690
## [3487] 26.649930 23.848108 34.427799 28.499081 29.563394 38.366586 29.709879
## [3494] 27.517023 23.726728 31.904455 29.309786 33.715878 32.319577 30.732906
## [3501] 27.786373 31.841955 34.583021 18.069823 22.452295 27.944271 34.497791
## [3508] 27.877905 33.203919 33.551551 25.686877 23.165534 28.646941 34.831942
## [3515] 30.383390 33.687604 39.885599 30.911912 30.395864 39.650769 27.160280
## [3522] 38.597712 25.904048 31.573411 27.038345 27.702828 35.368064 35.590468
## [3529] 25.452276 27.457676 30.094509 29.492097 33.577687 24.714399 17.923491
## [3536] 32.981412 28.936537 36.649095 32.058828 38.199319 24.884554 31.877028
## [3543] 28.973913 26.486128 34.980327 27.537687 28.574155 32.619199 34.633019
## [3550] 30.427551 32.376831 24.357965 30.539106 23.931381 33.934576 28.717255
## [3557] 30.430687 25.338700 30.066309 24.579488 24.599444 24.233710 30.935473
## [3564] 26.087154 29.074131 24.768346 36.325918 21.418746 29.645776 35.351062
## [3571] 34.694481 29.691876 41.921773 26.412144 27.656274 21.072456 34.647128
## [3578] 35.647863 29.154939 29.135358 29.613297 27.808203 34.143726 33.108355
## [3585] 27.320472 29.627859 33.811274 26.593152 27.980900 40.913699 24.755022
## [3592] 30.337693 30.023432 28.974972 38.130138 35.560230 33.614735 33.012772
## [3599] 31.431305 27.069798 29.075219 25.004841 27.524682 28.532866 27.013239
## [3606] 25.040531 34.865801 31.804431 26.622655 25.450332 22.197933 38.935319
## [3613] 30.291638 40.763426 42.454973 22.538728 33.792716 29.829905 25.472904
## [3620] 32.347585 32.263958 28.423991 36.335218 34.766056 29.446775 32.649322
## [3627] 26.016104 28.784855 25.762601 27.214446 30.580240 26.367458 35.298336
## [3634] 20.639690 37.391959 27.458228 29.469483 28.507206 32.089024 24.946954
## [3641] 31.966070 28.374768 27.655362 37.942756 22.184364 24.177982 23.909172
## [3648] 32.755924 26.558324 31.275870 27.847732 28.937577 36.749459 30.501792
## [3655] 23.530450 28.551289 29.910222 29.022860 25.598010 32.312085 31.147887
## [3662] 34.826119 26.484473 30.972775 33.679876 26.130464 39.358351 32.525808
## [3669] 23.077959 24.950014 31.559041 42.396082 32.421227 24.830112 28.693961
## [3676] 42.320869 29.597584 26.302727 29.830926 25.026633 22.309852 30.328081
## [3683] 30.585240 21.762196 26.032542 27.171907 34.279579 38.756257 34.809808
## [3690] 36.164566 19.137206 28.595662 23.761947 29.347984 25.472193 30.545968
## [3697] 39.254604 31.658732 35.608067 36.829083 29.908178 25.608606 26.188277
## [3704] 18.286208 23.564142 30.060201 36.216678 28.777174 18.431870 31.175483
## [3711] 32.960917 25.750781 34.089782 27.136586 27.338111 30.378706 25.299615
## [3718] 34.946081 31.868119 28.625110 22.593982 29.640475 29.845643 34.401405
## [3725] 32.854670 22.627256 29.048320 29.459379 23.054353 39.130465 26.033098
## [3732] 30.699989 17.896333 34.335940 26.411427 31.534806 31.142129 27.912945
## [3739] 29.744718 26.534497 32.850046 23.357196 22.652278 30.721158 21.890040
## [3746] 23.589498 29.735364 29.522335 32.649270 33.836410 26.766732 27.445128
## [3753] 23.001049 23.489474 30.984288 28.443023 25.566297 30.990611 43.665434
## [3760] 26.957819 29.308236 31.816057 30.401382 35.179611 32.768530 28.580502
## [3767] 27.238442 31.056167 39.233192 31.131277 30.988321 23.879530 28.811526
## [3774] 30.353247 25.017209 36.971128 25.437762 36.778348 21.931589 35.271347
## [3781] 29.413137 27.791566 30.125833 35.559125 27.953032 41.634178 27.416990
## [3788] 29.700405 26.356867 29.644993 29.914801 32.948695 30.058445 26.624768
## [3795] 30.401598 35.687723 39.136674 23.104047 31.180789 28.697834 24.917738
## [3802] 27.654786 29.812161 23.271802 26.405355 21.711401 27.080061 33.663793
## [3809] 27.655609 33.502189 24.024119 35.879115 30.296629 31.522202 25.088337
## [3816] 21.108018 27.250958 36.324550 29.559436 33.128109 29.193363 35.189303
## [3823] 39.206282 27.544498 27.391007 20.030006 32.065071 27.327289 27.958014
## [3830] 31.005318 25.725301 27.752943 17.184176 28.683828 30.942790 28.222130
## [3837] 28.586586 27.781130 24.323547 28.216858 26.356775 32.098923 17.573319
## [3844] 37.895244 26.106227 31.755302 26.854085 33.547686 30.677864 29.066432
## [3851] 28.024371 21.898872 26.731178 27.794862 25.458164 25.923186 28.179155
## [3858] 28.796958 26.199310 24.891363 27.842611 28.010282 34.079235 28.049089
## [3865] 29.549694 25.998955 36.677409 25.406704 26.633254 24.086648 29.911201
## [3872] 32.076097 37.083713 27.097661 32.119866 29.229110 26.258655 26.676440
## [3879] 26.646461 30.107829 27.515768 26.675681 35.137836 30.743515 28.501271
## [3886] 26.915364 41.863855 34.997529 28.845222 30.247954 28.350840 29.569371
## [3893] 21.177273 31.027655 26.425294 26.706930 27.787506 20.894443 30.467613
## [3900] 26.715682 44.145943 21.183872 26.643937 27.331404 27.484970 18.257057
## [3907] 33.350777 24.039079 31.681294 33.439144 34.037927 43.628585 33.478307
## [3914] 36.610121 34.580123 28.388185 23.839205 33.425122 29.097104 31.976104
## [3921] 23.877438 30.639399 28.682555 32.099237 34.702291 22.961606 31.312511
## [3928] 26.248828 31.075914 26.300248 26.319003 33.642814 34.463942 33.177248
## [3935] 31.730562 19.172083 31.440845 34.026335 30.666148 33.380516 35.420410
## [3942] 23.438931 28.561209 36.822452 21.120570 22.918221 28.955429 34.025464
## [3949] 23.454754 27.914016 23.500695 31.677249 23.716298 37.848370 28.526869
## [3956] 25.842233 27.257614 36.803701 39.306752 20.665201 26.287070 29.989489
## [3963] 36.825343 34.977241 25.932415 23.975031 22.819053 23.299752 30.727098
## [3970] 28.222584 30.968765 28.941710 34.870200 34.405016 32.221555 33.203702
## [3977] 30.194639 27.828432 25.343316 32.734973 26.765023 32.979576 35.635282
## [3984] 30.987533 34.401740 22.844685 38.612502 34.456514 30.865609 32.802776
## [3991] 29.321577 27.142699 23.950138 24.645132 38.494069 35.870964 21.321192
## [3998] 33.495041 28.961604 29.629272 31.961743 24.673519 22.029530 26.941910
## [4005] 27.697606 20.686757 22.536425 24.685625 28.170376 31.042069 27.120703
## [4012] 33.935629 29.493947 28.373776 23.894077 29.455199 34.590209 32.100638
## [4019] 37.548859 30.897105 36.417145 28.891947 36.412156 36.630629 13.897126
## [4026] 38.749099 34.074144 37.818907 33.706815 21.285813 31.066448 27.070073
## [4033] 28.763182 32.070608 23.350699 32.772979 30.134746 35.323458 28.219903
## [4040] 40.431749 30.771850 25.849817 28.838814 30.727503 28.805076 32.694358
## [4047] 30.690063 27.283124 26.714053 37.530238 33.635305 30.550959 31.402903
## [4054] 33.099490 35.484446 28.123896 26.107569 31.332222 37.523476 31.429666
## [4061] 33.947724 23.699365 24.604336 26.102005 30.922863 25.822112 29.181662
## [4068] 23.040247 30.937385 32.102570 34.998281 40.612205 27.062323 28.411935
## [4075] 27.571645 19.682314 31.059918 31.008646 27.316128 29.192527 23.210081
## [4082] 40.329152 32.451318 28.801500 34.264090 30.484384 25.265802 35.987203
## [4089] 22.910261 32.904237 29.004073 28.732514 30.416127 34.511316 23.444668
## [4096] 39.300005 31.720292 31.493987 31.161714 33.326442 33.455481 27.058451
## [4103] 35.209427 23.036107 30.835058 30.263880 28.604557 26.078838 29.500696
## [4110] 32.346384 25.391708 35.005933 26.411357 28.444218 27.727537 34.579626
## [4117] 29.500717 32.240902 29.074443 31.070782 31.301581 28.808740 29.938527
## [4124] 22.150428 27.633964 35.028413 29.622379 31.313797 22.863972 31.117054
## [4131] 25.302646 27.427352 31.879958 33.744959 30.113175 26.334824 22.750182
## [4138] 30.105535 34.337682 29.211899 30.976520 30.533886 30.538511 36.744595
## [4145] 32.494897 27.212097 33.869896 30.183324 25.643110 26.296583 25.249701
## [4152] 27.091327 26.215792 31.022466 32.538046 25.798251 34.766143 33.173862
## [4159] 25.901654 28.107940 32.143473 41.199083 29.799926 24.712907 28.378423
## [4166] 30.201653 30.139325 33.551476 25.433896 28.390198 37.990491 26.359196
## [4173] 33.476561 27.852869 26.775663 30.947674 25.605721 35.956892 21.768431
## [4180] 34.546429 28.146530 31.615784 29.158512 32.096362 34.154167 24.268287
## [4187] 26.203045 37.057523 35.418550 27.304841 30.095703 31.180177 24.628264
## [4194] 32.040955 25.226391 28.537263 27.140586 38.621395 26.598385 25.027333
## [4201] 27.743486 27.983014 28.647660 39.247262 31.877889 30.280597 36.843865
## [4208] 33.280336 29.678243 36.342960 34.449817 23.968107 25.531230 22.709066
## [4215] 31.080873 28.731224 27.713303 20.043409 29.587999 31.835423 31.761468
## [4222] 28.532942 19.397833 27.510366 21.832573 14.739521 29.485259 29.865485
## [4229] 24.976286 31.670811 34.594897 29.991376 34.193281 24.081686 24.851735
## [4236] 29.075367 32.307598 18.750272 33.126698 26.658802 30.827698 31.748707
## [4243] 28.958942 29.668136 28.073569 30.884322 32.350385 27.736462 29.148359
## [4250] 27.061771 35.582052 38.423405 32.439041 29.746550 26.506075 25.133915
## [4257] 27.340511 34.943498 40.248732 26.729971 32.226274 30.533159 27.902660
## [4264] 33.492909 28.991010 20.868325 38.356170 32.690419 35.494269 21.489681
## [4271] 32.961031 25.568062 27.404037 39.467896 22.089002 31.838111 37.966398
## [4278] 35.991099 32.593897 33.010659 34.419770 27.087109 31.398874 32.287569
## [4285] 30.565217 32.096202 27.326466 30.773327 30.183487 31.924585 25.221483
## [4292] 36.771756 27.391137 28.741457 27.124188 24.362401 32.579905 26.766677
## [4299] 22.711102 36.458829 28.301233 36.729410 31.679202 34.346777 27.071906
## [4306] 35.654053 37.115840 30.190922 33.132489 30.849590 28.559042 27.898534
## [4313] 29.710397 25.797663 36.121170 22.766872 22.865592 33.859726 29.069797
## [4320] 31.015370 28.761687 24.541105 23.782058 31.666805 30.027808 24.421799
## [4327] 34.738647 30.802288 29.929574 33.201861 32.441716 33.367573 21.215760
## [4334] 34.080134 32.573094 31.170450 36.113847 22.785111 34.480817 26.182973
## [4341] 30.269267 25.588109 28.065245 36.726148 37.105123 33.463628 29.059341
## [4348] 26.797134 27.075471 31.732468 29.212406 20.547265 23.605674 35.450630
## [4355] 32.734691 32.083333 31.698162 26.542556 28.449525 23.251597 38.359318
## [4362] 28.519457 36.864939 30.398035 34.538449 30.776421 27.168923 43.356766
## [4369] 27.007626 27.941999 33.196608 28.960681 23.810072 38.884864 30.255036
## [4376] 25.844870 31.044151 24.945422 30.181712 26.273785 38.941595 23.989135
## [4383] 25.019673 36.786217 35.467619 33.649637 26.058411 33.966227 29.553144
## [4390] 31.084530 30.086727 30.247950 32.241100 32.778558 31.391703 34.347370
## [4397] 24.394120 31.511787 26.851837 33.944436 25.232664 36.203876 35.113133
## [4404] 32.675590 26.972784 26.654696 26.518084 28.434856 28.777393 33.079900
## [4411] 24.237653 33.136009 41.734273 35.013163 32.717659 20.445154 32.613691
## [4418] 35.870331 27.238893 30.266635 25.635203 33.705499 27.752137 27.360078
## [4425] 34.310064 33.630690 24.175089 28.437008 27.442966 30.146669 27.046777
## [4432] 29.484457 37.428982 28.303359 34.173123 27.179020 26.888658 33.521403
## [4439] 28.948636 27.941215 28.736961 37.465397 25.693035 30.532466 31.982938
## [4446] 21.802026 29.937802 36.931794 33.541581 24.064032 27.644503 32.331632
## [4453] 35.736110 30.260686 25.939834 42.073112 24.266452 29.752357 33.093164
## [4460] 37.592947 17.753997 30.688452 29.271875 37.662631 31.956607 26.686978
## [4467] 32.300213 23.265859 41.904874 23.955056 33.561640 28.360012 21.357547
## [4474] 24.054967 40.825996 29.736607 19.478462 29.296085 28.203404 23.484979
## [4481] 34.041445 32.557381 25.292494 27.046155 32.689915 28.758313 32.639593
## [4488] 33.543952 26.201087 34.759306 26.900592 43.117658 30.554511 35.167134
## [4495] 24.618072 34.637488 25.534348 30.183573 22.736554 25.385302 25.421852
## [4502] 31.446842 43.554509 42.864851 29.538979 42.206377 30.982125 29.602666
## [4509] 23.968102 25.430953 29.115453 35.812791 26.737357 31.467820 32.469720
## [4516] 25.894848 30.815081 32.868756 20.105670 33.448333 27.297334 37.454445
## [4523] 24.706569 31.373378 22.578134 19.378032 26.641669 37.136427 29.126865
## [4530] 32.232537 28.693456 37.668470 41.025992 25.194885 29.799401 34.226142
## [4537] 35.867150 31.543317 33.888257 22.762387 30.025003 39.877141 27.012852
## [4544] 32.400512 29.006487 18.015865 27.386272 34.865569 30.804887 34.971525
## [4551] 43.327141 29.224093 24.819244 22.854087 29.360524 25.829486 30.590773
## [4558] 34.572026 27.104576 29.673856 30.574658 27.561149 20.339452 31.540997
## [4565] 34.128049 20.165199 32.228426 26.685410 25.937619 37.485883 30.841529
## [4572] 28.906558 34.946212 31.688008 34.868795 28.703088 36.340132 26.120814
## [4579] 27.631333 35.961995 28.200010 39.063594 37.101912 29.546278 28.544041
## [4586] 23.953003 26.532162 26.948090 30.144392 31.950668 17.921773 25.900809
## [4593] 25.297794 29.498053 30.160180 37.076693 43.320373 26.677886 28.289158
## [4600] 28.203119 27.162146 30.106855 25.850145 25.422162 29.961399 31.603418
## [4607] 31.981872 29.322373 31.614026 37.192544 27.215105 30.920712 25.431031
## [4614] 36.034152 26.851712 32.988036 32.536127 30.193099 24.379195 34.569920
## [4621] 31.878188 26.466260 32.839265 32.832222 22.389199 35.238457 18.944077
## [4628] 33.648315 35.111333 35.500371 29.570462 27.704566 40.131767 29.567824
## [4635] 43.026295 28.443485 35.671442 35.605426 30.847521 28.020882 28.610458
## [4642] 27.185404 19.651575 26.151996 39.081135 33.597887 30.168219 36.545005
## [4649] 37.352448 28.914503 30.077434 30.691587 30.178841 33.171955 31.427071
## [4656] 26.725503 25.735443 35.634148 28.458290 33.518182 35.243268 27.894794
## [4663] 36.340188 35.871660 36.007493 31.716291 25.723797 38.307949 33.601294
## [4670] 32.400812 20.471427 22.648004 38.607509 31.541714 34.597998 36.174802
## [4677] 28.513284 45.146902 32.414189 32.188372 26.474343 34.548886 29.548434
## [4684] 37.354710 25.518318 24.736550 34.140187 34.330636 29.942416 25.392310
## [4691] 37.348845 27.313872 27.534211 29.408143 31.372440 31.232013 41.024682
## [4698] 31.291425 34.951749 30.062025 27.745014 36.921059 24.835655 23.000676
## [4705] 25.696740 29.128488 34.835235 33.796826 30.481674 30.273868 31.613973
## [4712] 33.152156 27.510413 36.772114 36.930303 35.774547 28.578052 35.864161
## [4719] 32.690531 31.181488 38.325364 22.755165 34.811363 26.430813 34.002031
## [4726] 30.681452 23.192034 33.228953 30.152131 33.413082 36.517191 30.856095
## [4733] 33.543873 24.454749 27.004820 29.074287 33.212743 30.273590 31.960141
## [4740] 38.369727 32.675342 24.786647 28.779820 25.768797 29.951134 25.116216
## [4747] 28.351476 20.740155 22.511154 32.682092 23.453446 31.214550 30.002818
## [4754] 33.009503 37.795454 34.659415 31.917058 33.854450 31.726335 35.865755
## [4761] 26.982241 35.602262 22.528478 29.663215 25.704624 20.405538 26.488106
## [4768] 32.939229 30.421930 38.810509 28.645246 24.132158 33.174149 33.486346
## [4775] 37.409467 29.900440 35.863177 31.150380 34.923267 18.056834 30.724407
## [4782] 29.101176 23.194874 23.566803 30.296759 30.723639 37.388620 24.151260
## [4789] 36.850140 33.942418 35.946049 36.269537 24.890998 24.636610 22.729950
## [4796] 29.653693 28.022829 29.423432 34.263547 25.954122 24.724281 24.069518
## [4803] 30.276856 20.943799 32.276361 29.987329 27.438233 35.706925 36.361279
## [4810] 30.707185 41.390417 32.081987 35.495745 24.124784 29.982775 29.705917
## [4817] 34.912056 28.835620 30.539765 24.579002 37.559407 36.611241 30.542770
## [4824] 29.607787 32.382695 28.162053 26.801396 31.750849 26.609907 32.829520
## [4831] 39.235403 22.700953 24.002722 28.402364 37.762343 32.040639 26.171053
## [4838] 31.185377 24.638297 20.135523 32.351231 30.044692 30.945476 36.834251
## [4845] 27.531966 32.257315 29.172367 30.584752 26.639314 36.440014 33.314285
## [4852] 34.095339 30.943990 32.079180 26.830116 24.390092 30.687871 27.740772
## [4859] 25.761994 21.120751 35.519784 26.265169 31.370261 29.384020 33.187629
## [4866] 28.747527 32.644256 24.676017 34.374414 31.179101 35.627588 33.892145
## [4873] 28.101513 23.141197 25.027792 30.747239 33.270577 26.618987 27.818613
## [4880] 22.864358 30.026138 21.206083 28.088264 28.493612 30.582210 21.004476
## [4887] 25.142703 35.771832 23.054750 31.066530 30.068838 28.557759 34.796388
## [4894] 25.568486 28.153961 21.859465 35.760918 26.565159 26.758859 25.772365
## [4901] 30.688856 26.865354 24.592766 30.620093 30.498791 18.616481 31.299113
## [4908] 36.760769 30.827707 31.430724 31.058199 35.737310 31.986725 40.229742
## [4915] 26.608728 24.423122 29.796008 28.270207 36.941207 30.021985 31.642719
## [4922] 30.134114 28.797894 33.121481 37.024705 21.144216 26.054922 33.261145
## [4929] 36.165409 32.781642 27.003416 28.270276 32.969692 24.180388 28.514082
## [4936] 22.954926 31.347164 30.034726 25.196828 30.217508 27.350097 36.908308
## [4943] 40.136862 26.246121 28.941810 22.816764 28.267145 35.146062 29.185790
## [4950] 22.584101 28.844029 34.802057 34.343937 27.834115 33.063292 29.651088
## [4957] 27.490974 41.457490 33.851083 28.004853 28.693638 30.543943 41.193508
## [4964] 35.829516 30.129472 28.850441 24.115305 35.612563 28.283162 29.125838
## [4971] 32.947639 25.660327 27.880592 31.088429 25.576892 33.754751 23.973753
## [4978] 31.799060 31.623832 28.800440 34.740287 27.320261 24.090738 25.281669
## [4985] 34.244280 29.672589 33.703702 32.130710 31.453241 35.138502 36.844127
## [4992] 41.514384 19.366786 32.414608 29.129696 31.842298 32.574462 27.344333
## [4999] 34.962763 20.437752hist(ticket, main="Distribución del tiempo promedio para resolver un ticket",
col = "pink")
prop_mayor35 <- mean(ticket > 35)
prop_mayor35## [1] 0.1514Interpretación: El tiempo que tarda un ingeniero en resolver un ticket se concentra alrededor de los 30 minutos, siendo común que las atenciones duren entre 25 y 35 minutos. Aun así, aproximadamente un 16% de los casos superan los 35 minutos, lo que evidencia que aunque la mayoría de atenciones se realizan en el tiempo esperado, una fracción considerable requiere mayor dedicación.
4. Tickets escalados a segundo nivel
Un 20% de los tickets requieren ser escalados a un nivel superior. Suponga que en una hora se reciben 10 tickets. a. Simule 1000 horas de operación. b. Cuente cuántos tickets son escalados. c. Grafique usando la función barplot
set.seed(1610)
tickets<-rbinom(1000,10,0.20)
tickets## [1] 3 2 3 3 4 4 2 2 2 2 3 3 3 2 4 1 0 3 2 3 1 2 4 4 1 4 2 2 2 2 3 1 0 1 1 1 3
## [38] 2 3 0 1 0 1 2 1 2 4 4 2 3 3 0 2 3 2 0 0 3 0 3 1 0 2 3 1 4 2 3 2 1 3 2 3 1
## [75] 4 0 3 1 5 3 1 3 2 1 1 3 1 3 2 2 0 3 0 3 1 2 3 1 3 2 2 1 0 0 0 1 2 2 2 1 3
## [112] 6 0 0 3 1 4 0 2 1 3 2 1 0 0 1 1 2 2 2 1 0 3 1 2 1 3 2 2 1 1 5 1 4 3 1 1 1
## [149] 3 1 3 2 2 1 4 2 2 5 2 3 3 1 3 1 2 1 1 2 4 3 1 1 6 1 2 0 2 2 2 4 2 1 2 5 2
## [186] 5 3 2 2 3 3 2 2 3 2 1 2 2 2 3 2 3 3 2 1 2 0 2 1 1 2 4 3 0 0 2 3 3 3 5 2 1
## [223] 3 2 1 3 1 5 5 2 2 1 2 3 3 2 4 1 3 3 0 2 3 1 2 1 2 2 2 0 2 2 3 5 1 1 1 0 5
## [260] 3 6 2 1 2 2 2 1 3 3 1 3 3 2 1 2 3 1 1 1 2 4 2 2 3 3 3 2 3 4 0 1 4 2 1 2 3
## [297] 0 4 2 0 4 3 0 2 1 4 3 2 0 0 1 2 3 0 3 4 2 3 1 0 2 0 1 2 2 1 3 1 2 0 1 0 2
## [334] 1 2 3 1 2 2 2 5 1 2 6 0 4 1 2 0 1 3 1 1 3 0 1 1 3 2 4 1 0 3 5 1 3 2 2 2 1
## [371] 1 3 1 4 2 3 3 1 3 2 2 2 2 3 2 3 2 4 1 3 2 1 0 1 0 1 1 3 2 2 2 2 3 2 1 2 0
## [408] 2 5 2 2 1 4 1 2 3 0 1 4 0 1 1 3 2 4 3 1 1 1 2 3 2 2 2 1 5 3 3 1 5 1 3 2 3
## [445] 1 3 3 1 2 4 2 1 3 3 3 1 4 1 3 2 2 4 0 2 0 1 4 2 2 3 3 0 3 3 1 0 1 3 2 2 2
## [482] 3 1 4 1 1 3 5 0 0 1 2 1 2 1 3 0 3 4 2 2 1 0 4 3 1 2 3 2 3 3 3 1 1 3 3 2 0
## [519] 2 0 1 2 5 5 0 1 1 3 1 0 3 3 2 3 3 1 4 1 5 2 2 3 1 5 0 3 4 2 1 2 6 0 4 3 2
## [556] 1 0 1 3 3 0 1 0 2 0 2 2 1 5 1 4 1 4 1 0 4 4 2 4 1 2 2 3 1 4 3 1 3 3 3 3 2
## [593] 1 0 1 0 2 0 4 2 1 1 1 2 2 0 5 4 1 3 2 1 0 2 0 3 1 1 2 2 3 2 1 4 1 2 1 1 0
## [630] 3 3 1 4 3 1 2 3 1 2 1 3 2 5 3 1 2 1 3 3 1 2 3 3 2 0 0 3 3 3 3 2 2 1 4 2 3
## [667] 2 0 2 2 3 1 1 2 1 0 2 3 3 3 2 1 0 0 0 3 2 2 3 0 2 4 3 2 4 2 2 4 2 2 4 2 3
## [704] 0 2 4 3 2 1 3 1 2 0 2 2 1 2 4 0 2 4 2 2 2 3 2 3 0 3 1 2 1 1 2 1 5 1 1 0 3
## [741] 2 1 5 0 0 2 0 2 1 1 1 4 3 3 3 1 3 1 0 1 2 4 4 2 0 2 2 1 1 1 1 1 3 1 0 1 3
## [778] 3 2 1 1 1 3 1 1 2 3 3 1 3 4 0 4 1 2 2 2 0 4 4 0 2 2 2 2 3 2 1 1 3 4 1 2 2
## [815] 1 2 3 3 1 0 5 1 3 3 2 1 1 1 2 2 3 1 2 2 1 1 5 2 4 4 3 1 5 2 2 3 2 1 3 1 3
## [852] 2 3 2 1 2 2 5 3 0 2 4 3 0 3 0 2 2 2 2 3 5 3 1 2 2 2 1 2 1 2 2 1 1 2 2 1 2
## [889] 2 1 2 2 0 1 1 3 4 3 0 0 1 1 3 1 2 0 1 0 2 3 1 2 0 1 3 1 2 1 2 2 5 1 2 1 0
## [926] 2 2 2 3 3 2 1 2 1 1 2 1 3 2 3 3 0 2 0 1 1 1 3 4 4 2 2 1 0 2 3 2 4 0 0 2 0
## [963] 2 1 3 2 2 1 2 1 4 1 3 0 1 3 0 2 1 3 4 1 1 1 1 1 0 3 3 2 2 2 4 3 1 2 3 1 2
## [1000] 4total_escalados <- sum(tickets)
total_escalados## [1] 1998hist(tickets, main="Distribucion Tickets escalados a un nivel superior ", col = "blue")
freq <- table(tickets)
barplot(freq,
main = "Tickets escalados a segundo nivel",
col = "green",
xlab = "Tickets escalados en una hora",
ylab = "Frecuencia en 1000 horas")
Interpretación: De cada 10 tickets recibidos en una hora, en promedio 2 necesitan ser escalados. En las 1000 horas simuladas se confirma que cerca del 20% de los tickets requieren atención de un nivel superior. La mayoría de las veces se escalan entre 1 y 3 tickets por hora, lo que refleja una carga constante para el segundo nivel de soporte.