Taller: Simulacion de variables aleatorias no uniformes en R
Sebastián Rivero
2025-09-17
Taller Simulación de Variables Aleatorias no uniformes en R
Contexto
En un centro de soporte técnico de una empresa de software, llegan solicitudes de usuarios que deben ser atendidas por ingenieros de sistemas. Se quiere modelar el proceso de llegada y atención de solicitudes con distribuciones de probabilidad, y simular el sistema con R.
Punto 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
llegada<-rpois(5000,5)
hist(llegada, main = "Distribucion de llegadas de solicitudes por hora al sistema", col ="yellow")
prob_empirica <- mean(llegada < 3)
prob_empirica## [1] 0.1276Conclusión
La simulación de 5000 horas muestra que el número de solicitudes por hora sigue una distribución de Poisson con media cercana a 5, concentrándose alrededor de ese valor. Además, se pudo estimar la probabilidad de que lleguen menos de 3 solicitudes, confirmando la coherencia entre los resultados empíricos y la teoría.
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Punto 2:
Tiempo entre llegadas
El tiempo entre llegadas de solicitudes sigue una distribución Exponencial con media 12 minutos.
- Genere 5000 tiempos entre llegadas.
- Represente el histograma.
tiempo_fallas<-rexp(5000,12)
hist(tiempo_fallas, main = "Distribucion de tiempo entre llegadas con media de 12 minutos", col = "green")
Conclusión
Los tiempos entre llegadas siguen una distribución exponencial, concentrándose en valores pequeños cercanos a cero y disminuyendo a medida que aumenta el tiempo, lo que refleja la naturaleza aleatoria y continua del proceso.
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Punto 3:
Duración de la atención
Cada ingeniero tarda en promedio 30 minutos en resolver un ticket, con una desviación estándar de 5 minutos.
- Simule 5000 atenciones.
- Grafique el histograma con la curva normal teórica.
- Determine la proporción de atenciones que superan los 35 minutos
set.seed(0731)
life_time<-rnorm(5000,30,5)
life_time## [1] 34.40633 26.71436 32.02754 32.42586 31.03440 28.38515 34.68088 23.91538
## [9] 34.13022 40.59535 33.56756 31.24002 32.94123 27.10144 30.48544 17.51690
## [17] 13.88723 39.69527 32.00796 31.36991 26.10988 27.07967 28.10608 28.03457
## [25] 32.96574 24.56975 37.35242 34.17625 35.28869 27.15798 34.49966 29.68201
## [33] 33.54829 21.08416 31.61464 26.90709 28.81525 21.21220 24.33543 31.52928
## [41] 28.54421 33.65272 36.26562 32.04334 20.40688 16.58422 35.84237 29.05861
## [49] 23.02926 36.45781 21.75919 43.61936 28.95250 28.06347 35.93076 32.31961
## [57] 37.70481 35.76527 34.94196 20.31448 24.26290 41.32650 31.24649 31.31263
## [65] 26.41872 32.49857 35.12783 34.38863 35.08324 21.88168 32.69683 29.20056
## [73] 23.66037 29.83223 29.37673 34.78809 26.60727 30.05554 25.22249 27.72065
## [81] 31.94445 30.52685 22.52793 26.85057 21.93262 30.50747 23.04921 25.70781
## [89] 38.33525 32.19489 22.24831 31.48405 24.49991 33.89151 33.41060 28.42098
## [97] 40.58371 24.69259 19.20611 29.50126 31.06126 25.55628 26.70658 22.64843
## [105] 31.36057 26.08984 31.03961 32.29736 26.61649 35.40638 36.31729 25.47504
## [113] 36.92772 31.90041 38.84874 27.02356 27.78132 26.20322 27.79810 36.06769
## [121] 35.39944 32.21551 34.46320 31.97493 33.63997 30.06029 24.63424 28.05624
## [129] 34.37883 32.86974 31.73615 31.50935 22.76652 38.76798 34.20607 26.12301
## [137] 31.51892 26.26942 37.83989 38.85856 34.17244 30.24901 37.27742 33.75730
## [145] 29.42311 16.32177 33.92403 30.23939 35.53255 25.21869 34.62183 28.76176
## [153] 35.19243 26.16783 28.38043 26.58085 29.10864 35.20914 28.12389 35.88685
## [161] 34.03056 34.45935 27.55601 25.55666 22.57800 35.44605 28.32957 26.04854
## [169] 22.64589 26.42370 27.62072 31.71238 32.75350 28.44995 30.59897 20.61463
## [177] 20.38242 22.20268 24.50517 29.69547 24.93374 40.01864 36.90489 34.52034
## [185] 34.69270 38.29135 39.51518 28.93962 37.86650 32.19986 29.36143 24.97343
## [193] 21.54898 31.41571 32.37489 30.18907 27.78144 27.10022 33.72562 31.60187
## [201] 37.00807 30.86687 34.00224 23.04115 28.86602 25.44097 43.22038 27.22076
## [209] 22.70453 32.84263 25.54133 29.23155 35.48184 25.33346 23.11032 30.48043
## [217] 28.15822 28.97603 32.49555 32.12712 29.63168 34.59237 32.18139 30.83293
## [225] 24.28295 29.43423 35.57346 29.01389 31.22967 31.58659 29.17640 35.78138
## [233] 28.77272 38.39743 35.25652 26.56955 24.73410 35.12391 24.80609 28.10713
## [241] 26.23794 31.81043 25.27277 31.98698 35.13337 37.05448 28.88236 32.31353
## [249] 39.88779 27.91019 22.09056 38.40984 34.32892 26.08091 30.19170 27.34476
## [257] 28.44944 31.35654 27.54085 20.69994 36.21602 39.53366 28.38043 33.91459
## [265] 23.78042 20.93994 29.48200 25.83457 33.56801 30.28109 30.59580 30.28553
## [273] 26.55763 33.95976 25.03318 32.03274 26.70714 27.78884 23.30485 27.59007
## [281] 29.93433 26.56053 33.08619 19.90387 30.01014 28.78917 17.55914 22.55113
## [289] 31.38123 30.73571 25.30691 24.45528 28.12486 32.56457 32.90428 31.54505
## [297] 35.14068 39.77459 24.51828 32.97373 24.23295 29.49928 31.24775 30.20716
## [305] 28.59692 21.26405 29.35170 43.99240 30.14061 27.98319 27.81824 29.85344
## [313] 40.01076 21.70465 33.32190 27.91215 22.98371 36.82536 38.90882 29.82027
## [321] 29.09088 33.32239 32.60138 27.19899 27.61356 34.03401 22.02907 31.34967
## [329] 35.36345 26.75343 34.69554 31.07587 27.81568 28.22963 23.42330 28.30292
## [337] 35.43669 29.95153 34.57493 32.75334 23.96214 33.22479 32.00994 26.66204
## [345] 35.12922 17.56116 30.41708 22.48400 26.10100 20.88891 26.11859 50.39082
## [353] 31.27989 31.78656 39.49426 32.97667 25.73656 35.73233 31.04060 24.43159
## [361] 39.47537 35.92122 28.36532 27.96365 32.96608 28.04479 33.32664 42.43903
## [369] 35.28465 24.22928 35.40732 31.98610 30.96076 29.36892 31.80523 30.62494
## [377] 25.62574 22.47102 27.17227 24.34657 26.24153 22.12978 34.31565 25.21743
## [385] 31.81453 25.29163 32.83670 30.21051 22.35691 29.16606 30.70386 27.57756
## [393] 29.23823 30.85999 23.23090 14.15632 30.40391 31.09698 26.01007 26.14370
## [401] 23.04348 25.89307 35.04910 25.57536 24.48983 27.86714 31.53779 24.90101
## [409] 30.72728 24.94047 24.09044 27.54508 26.15941 28.61479 28.90950 32.76118
## [417] 34.32548 26.88391 29.59970 30.80436 22.73487 35.49071 35.94340 29.38455
## [425] 24.32619 28.35967 34.47155 32.39350 37.78782 24.16432 31.29836 25.15353
## [433] 33.63387 32.62423 42.01854 22.44659 29.85445 20.13264 30.23079 28.25356
## [441] 22.63282 29.71753 28.44415 38.13055 24.91749 38.16746 36.23403 32.05845
## [449] 31.07030 30.66644 34.47858 28.77817 21.06716 28.32031 28.19688 27.90782
## [457] 37.09620 32.06904 23.89731 22.47119 20.52118 26.52348 31.12460 25.09227
## [465] 32.34050 29.86137 30.89525 38.31055 28.71443 25.08709 26.85416 26.33457
## [473] 25.50504 26.51401 33.73867 38.27244 26.34752 31.11842 26.73500 29.28881
## [481] 22.06456 31.07321 26.40704 18.66578 30.41548 34.23749 34.42045 27.31798
## [489] 26.36500 32.66566 25.96559 26.07632 32.80343 30.78786 30.29090 35.68800
## [497] 29.40474 31.01658 27.27623 40.22581 31.47442 23.62155 26.98571 27.79442
## [505] 26.69990 33.61663 38.47839 23.50100 28.51899 36.23521 24.87178 28.81339
## [513] 22.67902 21.73563 38.28700 31.23105 21.48974 31.85373 26.75184 27.47813
## [521] 16.24614 34.65246 23.50499 25.26757 30.84753 28.05142 36.45048 39.22239
## [529] 20.61775 29.68689 24.54902 26.17723 28.06208 36.14519 32.55096 24.37410
## [537] 33.97277 39.32818 26.20343 28.56549 31.57823 25.52459 26.68844 22.13091
## [545] 30.16143 24.91764 31.20347 35.69045 29.14310 26.37804 30.89059 33.22470
## [553] 26.97784 30.67113 28.93726 26.42765 38.11431 33.17014 32.26137 33.55998
## [561] 27.99882 36.01889 36.66718 37.24111 30.93707 28.86313 26.58299 32.04719
## [569] 24.05958 29.41485 34.53828 25.24481 33.47733 43.25188 35.46581 32.81093
## [577] 36.08780 26.64009 38.98521 28.43612 24.67306 27.26752 33.63408 29.97586
## [585] 30.41479 32.94562 34.43680 36.24849 40.16694 31.39521 26.27015 31.70108
## [593] 17.38452 28.68517 34.88722 22.68241 41.21508 39.70132 36.20310 32.72168
## [601] 21.86072 30.12399 27.79749 35.72916 26.78975 20.33370 27.42814 37.91812
## [609] 27.98343 31.46261 23.10380 35.23492 26.78659 22.96252 32.09852 37.55487
## [617] 26.89831 33.72088 27.35890 24.90961 28.94757 22.69397 34.08936 32.42917
## [625] 30.90903 34.76220 33.98994 38.75479 28.66480 29.52651 30.83230 38.02620
## [633] 34.43158 31.50523 30.63662 26.27910 30.82056 28.04789 31.78623 27.55035
## [641] 28.37811 25.98567 34.25336 29.63397 33.29200 25.13084 30.35466 37.77427
## [649] 39.71599 26.82734 32.91048 18.88231 27.61398 27.20046 34.91427 37.70264
## [657] 24.38100 22.13002 29.63377 29.29135 23.76270 34.55919 25.63643 28.72012
## [665] 23.96965 23.64791 26.06202 30.02040 26.53221 27.46502 34.15251 31.41628
## [673] 26.89729 26.50255 38.59419 28.88299 27.05699 31.77038 21.07643 28.89236
## [681] 29.13436 35.99626 22.29237 25.52717 30.20164 23.44975 35.82916 28.57279
## [689] 23.08675 21.24160 36.10636 30.96897 31.04713 32.36139 25.63541 25.29966
## [697] 16.81716 30.97326 34.39052 27.91914 29.19527 29.96623 37.33163 22.63284
## [705] 26.80417 26.97638 29.00199 25.79236 24.33313 20.91863 23.60759 30.94647
## [713] 35.68133 27.07417 27.14749 36.92267 30.62601 33.05718 33.42943 33.94294
## [721] 26.21910 32.83564 25.72168 29.08954 20.62081 27.32947 24.22485 26.82359
## [729] 34.13867 24.91683 24.82967 32.59339 33.79996 21.34696 35.93728 28.92095
## [737] 32.92294 18.08411 29.90413 36.90104 22.41991 34.29909 24.63821 21.96407
## [745] 25.49168 27.47745 26.11489 24.98652 25.75312 25.52253 30.58935 30.46109
## [753] 25.84156 25.99148 38.43656 21.06762 32.05287 31.07961 36.88837 22.08614
## [761] 28.04514 29.64678 33.48930 27.55471 26.63500 29.11295 21.55668 34.46273
## [769] 25.64688 31.90927 26.41875 20.87268 31.99234 24.68187 34.59716 36.07621
## [777] 25.05791 43.32662 27.93413 35.35484 22.57301 39.71192 28.94383 30.77521
## [785] 23.98399 26.73063 28.94155 30.61918 27.46731 28.77429 29.31008 20.97119
## [793] 27.96703 31.14194 26.75201 26.00384 32.06943 26.89400 30.54939 28.51560
## [801] 29.03766 34.17630 33.80404 23.34577 23.70449 27.91191 28.96679 32.89533
## [809] 32.98566 28.69827 22.65139 39.04228 32.08685 33.12640 25.66318 23.47585
## [817] 28.48810 30.72755 31.16498 26.48973 27.73984 28.96621 37.71330 25.14460
## [825] 29.48494 22.77603 25.64449 31.16740 26.45925 25.35173 32.38337 32.41510
## [833] 30.95946 31.14696 25.64101 20.47141 21.84335 28.50167 31.38153 26.25900
## [841] 26.76435 26.94675 30.53839 30.07493 34.90978 29.37391 39.37779 30.29060
## [849] 20.42104 25.83989 29.95840 22.34245 36.89713 24.49033 32.49086 24.85318
## [857] 25.12897 31.25992 17.25947 36.25220 25.21227 35.44271 21.32382 29.20377
## [865] 21.50074 26.77416 29.92023 34.31553 26.96289 28.02257 25.65805 16.77132
## [873] 31.90450 36.68250 28.71039 28.82506 32.38396 36.64130 34.38398 39.86254
## [881] 28.92734 29.36766 31.12297 26.50447 32.80377 37.28333 32.53893 27.85404
## [889] 27.93870 29.34889 29.27446 36.99207 25.55359 31.27193 42.85082 16.08412
## [897] 27.75714 32.72328 32.43685 34.10161 33.82573 33.08512 28.15787 30.15110
## [905] 22.15177 38.18982 30.55945 24.86488 32.26195 28.55901 31.05722 31.91754
## [913] 35.99682 31.28873 25.61235 26.83808 35.42275 14.82808 28.75825 24.57703
## [921] 22.65976 28.07288 35.49204 25.14985 21.91528 32.62533 35.08240 28.77272
## [929] 25.65187 33.97847 35.03922 33.82682 32.89075 25.18714 31.47721 29.67069
## [937] 25.26208 30.93368 32.51156 36.76048 30.64155 31.99590 31.36999 31.35617
## [945] 35.83997 32.37037 32.49906 26.99160 28.75416 27.81429 35.47750 37.37882
## [953] 28.62566 28.42467 31.68167 28.71010 19.39841 33.63439 23.31400 38.73159
## [961] 29.01537 37.94425 32.04288 43.24356 40.89618 18.13474 35.04820 31.09013
## [969] 30.73028 31.56638 28.33582 32.96538 23.34303 21.20793 30.75128 23.16114
## [977] 29.21600 28.38085 28.17224 26.83206 20.33599 24.34646 37.68190 30.11028
## [985] 35.90593 34.40698 35.27047 33.69082 36.22333 21.93171 25.70579 33.65889
## [993] 33.58417 26.60616 29.86497 26.39159 31.25926 25.10617 28.17917 33.07421
## [1001] 19.90279 26.74766 31.74053 28.94077 27.22856 23.89562 27.99862 32.86974
## [1009] 28.66821 34.79124 43.53594 24.76223 24.62654 33.22243 33.75230 27.12495
## [1017] 32.96926 31.67459 29.97490 32.79293 22.78998 24.71689 25.41953 36.53695
## [1025] 23.89492 26.24036 36.92049 29.57037 37.11432 34.37554 27.19743 33.84187
## [1033] 33.30613 24.46568 29.87421 23.26800 21.88084 34.99695 28.88115 24.56807
## [1041] 28.45109 20.25558 25.50548 27.96026 28.11026 31.16363 32.06301 31.99224
## [1049] 35.27093 26.55029 28.98903 37.03871 28.41564 28.56471 28.97136 35.70837
## [1057] 32.12918 29.23446 32.65500 27.55618 29.18525 31.06049 23.84443 35.32354
## [1065] 29.24674 23.56952 32.48140 30.25826 21.23277 23.47317 29.06596 25.76148
## [1073] 36.00420 25.77265 34.81085 28.16812 21.78685 29.20320 22.02654 32.12128
## [1081] 28.52930 23.22873 31.04168 34.65992 23.40941 30.98770 21.59109 23.04736
## [1089] 19.17002 30.12376 32.67470 28.51870 28.49613 34.45770 35.71710 25.45391
## [1097] 29.15563 37.08317 30.22441 31.54694 19.03393 23.60005 30.87281 33.35045
## [1105] 41.87914 24.26516 31.47851 37.48586 37.26674 26.41882 27.27838 29.90345
## [1113] 48.59568 29.41807 20.75169 20.37867 27.56087 24.94796 31.51118 38.02706
## [1121] 31.99988 25.93428 23.93709 30.98553 40.22813 24.98928 34.76027 35.75716
## [1129] 25.75435 30.57743 22.23164 29.93605 40.34180 18.85298 24.40333 34.48834
## [1137] 40.12834 36.07826 29.14651 27.23807 26.90751 35.49492 34.13751 36.89759
## [1145] 32.67597 38.46414 21.59288 29.26833 26.71270 28.06617 36.11518 18.81983
## [1153] 38.02467 22.69148 29.20828 31.74148 35.18559 40.75495 36.75852 33.46809
## [1161] 31.42106 29.60933 27.07095 23.49210 36.74824 32.72921 30.55877 22.16329
## [1169] 28.36100 34.27736 26.81724 34.65428 27.92901 25.40905 27.69614 27.91509
## [1177] 29.31192 36.85459 20.73165 31.07165 23.04881 29.30693 30.28115 31.37832
## [1185] 23.45937 22.03324 28.43617 28.57847 20.17967 21.14048 32.74235 26.65306
## [1193] 29.32427 34.58914 35.44957 28.96880 27.84053 21.17749 40.49174 28.89086
## [1201] 24.58209 26.23698 35.38858 25.95550 38.53444 25.20401 31.14852 28.43232
## [1209] 26.82938 25.09132 30.31063 34.43535 33.49855 21.37470 32.92401 25.37389
## [1217] 26.23772 20.56877 28.87276 24.43117 29.39463 34.22458 29.47876 22.96334
## [1225] 36.43892 26.84791 27.88635 27.53968 30.68780 20.45411 31.67977 37.84800
## [1233] 29.20311 27.71034 28.88257 29.45417 28.17516 26.38340 35.75435 39.47995
## [1241] 36.91049 36.55181 30.55235 30.02622 38.34574 24.10324 22.84755 31.87246
## [1249] 25.75661 32.09238 31.20789 28.17930 29.83591 30.46301 38.84374 24.43623
## [1257] 29.36108 32.02875 31.34678 29.12140 26.62173 20.07807 28.86967 26.24710
## [1265] 30.57562 31.55302 29.40140 31.48223 43.27096 28.71318 29.64918 32.97282
## [1273] 24.95896 28.38948 29.46119 26.77715 35.93909 35.13763 32.44971 25.06367
## [1281] 28.07568 31.95941 24.81041 34.71754 30.55686 35.94195 31.92324 31.56331
## [1289] 43.16909 30.69545 35.25158 28.04916 34.53565 31.24834 28.75953 29.25018
## [1297] 32.45830 27.70315 26.87439 36.65406 28.29915 32.08467 32.80552 23.10338
## [1305] 32.13015 31.96985 38.88166 33.67150 22.92716 40.45593 35.54755 28.27905
## [1313] 28.75890 29.45354 22.90147 31.30525 40.49600 29.90951 32.48316 24.61906
## [1321] 30.45143 32.29492 33.14442 36.71500 33.31916 37.94578 33.58539 30.78339
## [1329] 33.29659 31.22754 33.85897 29.56689 27.87171 23.61202 27.46752 25.63239
## [1337] 28.13406 30.62093 32.34481 28.22508 33.13795 38.36291 41.12252 27.25339
## [1345] 28.15282 35.81694 24.44680 27.19652 24.39360 24.86195 32.70488 31.18585
## [1353] 26.04802 28.51599 28.80652 34.72859 19.72173 29.05559 34.82875 30.50203
## [1361] 31.24752 30.89706 23.49475 33.38492 28.54658 40.01546 20.15924 36.77104
## [1369] 23.86132 37.92175 28.08660 30.64500 31.31406 28.66441 30.29721 32.79410
## [1377] 26.78559 23.83001 33.65184 41.40846 40.64782 32.56529 33.44911 28.14852
## [1385] 27.99606 24.72852 18.12852 30.34617 28.68844 34.66994 31.67298 26.25982
## [1393] 26.95163 25.28048 33.00403 35.10298 31.05444 32.59812 30.65617 29.70063
## [1401] 32.99608 34.80469 26.45057 28.06383 25.54992 37.00029 25.33469 23.92520
## [1409] 29.63630 22.07252 37.95159 28.50761 25.60618 29.84505 37.92973 38.97319
## [1417] 27.88080 34.88835 24.14496 37.18663 21.11127 23.88573 31.93544 25.70964
## [1425] 23.14090 24.57573 26.87645 26.68952 36.88861 18.53780 29.30881 27.63610
## [1433] 32.92073 35.52862 24.42526 31.57953 32.05749 27.47720 37.26009 44.59158
## [1441] 29.66729 32.45164 30.23432 23.61821 40.10556 29.23356 27.87816 27.73163
## [1449] 36.62491 24.98689 38.10093 37.54158 28.38366 28.03323 21.98063 36.41789
## [1457] 31.42978 33.14724 31.98225 35.04738 27.30195 27.62506 27.39995 28.97736
## [1465] 29.10165 35.61946 34.13274 28.45662 28.92125 29.35031 27.47080 27.52311
## [1473] 28.18766 32.16573 19.34423 32.79520 25.65609 18.43383 29.58240 27.49960
## [1481] 35.88858 31.24737 36.37674 31.77771 29.84602 33.56468 25.13623 32.16816
## [1489] 30.12877 34.66363 38.90674 22.78173 34.29819 40.03357 21.26879 32.14585
## [1497] 21.13798 33.72389 36.45753 27.36279 34.14898 26.07035 26.08538 37.32177
## [1505] 37.49934 37.72645 30.59975 37.51470 28.73747 40.79085 29.15499 37.18759
## [1513] 21.33155 28.39759 30.53924 23.42265 21.92869 36.10343 35.83300 34.68222
## [1521] 25.78230 28.46891 23.46039 28.31605 35.10219 28.02353 33.72630 28.64125
## [1529] 30.05532 27.74329 33.48904 22.36075 28.63115 31.55641 26.24403 26.14782
## [1537] 34.63150 35.01008 34.16386 28.87051 24.31685 40.54360 29.14172 35.77346
## [1545] 25.98084 25.00445 20.77527 31.12002 34.25283 32.36630 24.46880 25.60997
## [1553] 28.79533 29.18138 30.43537 24.54870 26.66541 28.16507 29.09055 27.77884
## [1561] 19.00791 30.73405 31.69266 30.86039 25.68473 33.39680 33.37535 23.07466
## [1569] 36.80065 27.88947 26.27006 36.21179 27.14610 28.32654 28.51391 23.40754
## [1577] 31.50397 27.77290 28.47877 19.72655 30.56385 30.33654 29.42721 11.32041
## [1585] 37.65737 32.78967 35.26212 40.54441 23.32980 25.17649 26.35565 27.00142
## [1593] 34.33321 29.44416 32.82678 26.99722 27.90281 24.07539 35.53749 33.36217
## [1601] 31.80124 29.34326 26.33119 23.98325 19.74216 27.77474 29.58471 34.40316
## [1609] 25.96722 30.49858 29.23610 34.68680 31.14191 28.77936 34.05914 28.16490
## [1617] 31.27656 28.09116 30.98120 28.28919 25.70572 24.73137 25.32233 37.79635
## [1625] 36.37025 23.67045 34.48267 28.13289 39.45213 31.55038 30.91978 32.54800
## [1633] 23.18711 35.87266 35.91989 32.33675 38.22427 36.56058 28.86591 30.59195
## [1641] 24.22715 27.22497 26.93854 35.86707 31.52099 25.80495 26.41951 34.31947
## [1649] 32.39802 36.56627 27.34847 26.27438 35.69602 26.47574 35.74689 29.32839
## [1657] 37.11171 23.80254 33.82052 29.59513 27.91819 35.82059 35.36708 37.72635
## [1665] 33.42149 30.70696 34.65671 36.03760 27.33742 29.17648 19.43899 32.97209
## [1673] 25.44751 34.62955 27.97611 21.85156 23.12186 26.05817 23.58510 34.29741
## [1681] 34.35480 29.47482 37.36804 23.55233 27.86715 32.62346 34.33916 21.92854
## [1689] 26.34515 35.89049 33.96614 28.24901 29.03266 26.17033 18.23233 25.50568
## [1697] 25.55702 20.37301 22.90426 26.08283 33.75201 29.78168 29.08414 32.80644
## [1705] 20.58487 35.02683 43.74627 28.26368 30.93725 21.70353 33.57644 26.72834
## [1713] 33.26586 28.45065 30.85115 27.74723 26.33029 35.36430 31.96308 35.73148
## [1721] 38.35586 30.81994 41.25554 34.40392 37.38862 30.67537 39.40204 37.05815
## [1729] 29.05297 30.41385 28.14501 29.41748 31.82127 27.01102 18.66412 32.49461
## [1737] 31.92150 33.16433 32.57750 33.25584 40.17370 31.90679 25.50968 27.85665
## [1745] 38.09375 29.73349 24.66622 26.59345 41.09993 26.69354 24.52233 29.25814
## [1753] 27.08170 36.00556 26.57295 26.80107 25.71729 32.69470 34.02452 34.39167
## [1761] 21.42997 28.36616 31.96578 31.67374 28.88149 26.84369 22.19159 24.28814
## [1769] 28.09353 31.23736 39.87390 33.17661 24.48727 27.45443 24.88035 27.36118
## [1777] 28.73910 27.47533 36.86282 35.51863 25.16210 30.86743 33.23477 26.91265
## [1785] 19.57044 29.04578 28.42992 21.71247 28.85213 28.17142 27.81187 39.64249
## [1793] 31.64081 33.42651 39.60372 26.76414 23.65207 33.32629 27.55022 33.54295
## [1801] 27.39105 33.30372 23.26030 33.57481 29.84398 35.77952 34.76158 32.81690
## [1809] 22.02696 26.66646 31.15858 29.02970 21.12288 35.69961 26.25011 34.69734
## [1817] 29.45026 27.43307 28.35478 34.37943 28.94350 29.48971 26.89070 22.57665
## [1825] 27.02171 35.26239 31.87154 22.61016 28.85764 37.93084 39.63706 29.57414
## [1833] 30.46751 31.80259 36.72451 34.86173 33.81584 22.19909 26.34907 18.62293
## [1841] 33.31995 31.74455 22.14711 30.84302 36.25197 32.28837 36.53852 21.45717
## [1849] 28.65806 32.65386 37.67743 30.39526 26.91294 39.45892 22.31798 37.76552
## [1857] 29.60813 39.39408 35.28369 34.38653 26.41890 26.25579 34.98075 27.16881
## [1865] 35.13773 21.07562 33.33158 33.02569 33.89789 26.31779 20.37297 32.03321
## [1873] 38.15841 31.47805 37.19341 32.64777 31.19626 28.04097 38.49366 23.91029
## [1881] 32.00050 29.77896 29.04982 26.13288 31.97499 29.06863 30.81970 28.11209
## [1889] 30.46688 26.60272 21.81871 29.75621 29.44449 32.22300 33.33763 25.04478
## [1897] 25.65149 35.80433 21.38284 23.81886 31.42912 31.66300 30.36743 25.15422
## [1905] 21.53302 19.69856 18.75848 29.92272 33.57275 33.87543 37.58876 29.27602
## [1913] 32.75586 21.04679 28.01668 38.51277 29.59369 28.47399 26.55077 28.51569
## [1921] 32.64360 24.59385 28.80674 28.43164 31.05911 35.39424 37.44316 29.41523
## [1929] 29.59835 35.20432 31.81090 27.28161 27.00389 34.96057 35.81520 29.65367
## [1937] 34.27103 30.86884 30.50098 30.52459 33.68814 31.15191 33.86688 31.09658
## [1945] 34.70519 24.37038 34.24448 30.18690 38.00095 33.81457 20.31104 36.61493
## [1953] 27.19144 37.81517 23.80555 31.91002 25.04973 29.21375 26.79441 23.31322
## [1961] 26.87743 23.64792 36.60012 19.44409 23.19825 26.44229 34.61134 35.27215
## [1969] 33.85357 33.50711 29.84401 38.26304 28.51033 29.16808 29.02413 29.27945
## [1977] 14.80717 32.05026 27.91579 32.68610 29.09922 33.44289 33.76627 25.66540
## [1985] 24.62035 23.51098 33.67819 24.10620 18.20974 33.25604 28.44225 32.13573
## [1993] 34.62335 20.33777 23.88411 34.52212 34.12500 31.82047 31.29057 35.25992
## [2001] 36.69902 21.76452 29.25121 34.71104 35.42635 32.91983 28.43387 35.30290
## [2009] 29.37945 39.45113 28.75645 28.48634 37.21510 43.72228 33.74868 28.96545
## [2017] 31.25832 26.67528 29.63019 45.16808 38.20375 34.81580 26.63019 45.39039
## [2025] 26.57877 16.70470 31.42939 30.17385 29.88802 30.63720 31.92318 27.11400
## [2033] 30.55499 28.15770 31.45379 31.74501 37.55444 23.67174 28.06137 32.76228
## [2041] 24.52716 32.36197 31.32008 24.45837 26.68062 23.70490 28.88552 31.59582
## [2049] 36.60301 23.24529 30.96537 37.82064 28.82950 32.31166 27.31509 34.96484
## [2057] 33.16845 35.39216 21.24246 21.92265 29.95571 27.16587 32.65058 27.97725
## [2065] 31.05325 35.65197 24.78708 34.85261 24.66225 23.99730 22.30850 42.69294
## [2073] 28.99993 28.19359 28.23498 22.00600 31.88607 25.68426 31.10205 29.37286
## [2081] 35.82437 22.74127 34.84663 28.95346 39.78399 31.56132 33.28865 36.85804
## [2089] 39.12888 27.18760 33.35731 27.74508 36.28349 36.03536 28.54423 34.85501
## [2097] 28.80074 33.79534 30.47538 36.26911 30.94760 26.93696 23.11154 34.88612
## [2105] 34.43148 26.56626 35.63572 25.87782 29.08074 28.14072 33.67649 31.72206
## [2113] 30.73043 20.14278 22.24104 29.78652 29.74930 30.07695 33.54362 24.83012
## [2121] 27.52765 30.17993 32.80629 27.04527 22.77440 33.22100 34.45237 34.54801
## [2129] 25.73711 37.33531 24.80808 34.47857 32.64577 18.89212 25.55480 28.87354
## [2137] 34.36899 30.64284 30.47031 29.40243 32.34631 33.53701 32.89098 42.70457
## [2145] 25.09349 32.03894 34.57064 38.47893 31.44466 37.50327 35.38570 27.96697
## [2153] 26.93804 28.16899 33.35092 26.12853 30.20837 29.04396 31.40814 31.97195
## [2161] 33.38972 35.48509 30.35533 30.81727 34.15430 29.96483 22.51769 33.74797
## [2169] 30.68681 21.42882 26.28131 33.28083 28.75579 28.50304 27.36065 25.33891
## [2177] 25.54364 35.51087 25.04187 31.64368 22.19793 37.70114 34.43030 33.50692
## [2185] 27.50581 22.28067 33.00220 36.17201 34.03278 16.77952 29.51354 25.79590
## [2193] 17.74882 25.69515 36.58187 33.93404 29.72968 25.62376 29.70987 34.21329
## [2201] 27.18959 31.49757 32.59577 30.17905 32.95838 28.43251 30.12233 33.03577
## [2209] 25.41061 29.05197 26.16120 31.20034 30.88076 32.16930 36.32968 27.63837
## [2217] 33.57132 36.07357 35.56366 24.93002 28.80545 37.59086 27.06503 32.46277
## [2225] 33.35278 34.45149 37.88701 32.12564 30.47663 31.86531 24.39438 34.39104
## [2233] 26.43647 32.01996 33.91887 35.22689 25.21237 29.81312 22.84688 37.91424
## [2241] 20.55892 30.32925 29.54347 37.41603 33.26015 24.54162 27.05160 25.49820
## [2249] 30.51433 24.26325 23.31229 31.21826 30.79537 33.96866 28.02901 27.85758
## [2257] 29.03617 28.89994 26.86961 27.19242 26.09729 29.99272 30.17240 29.28686
## [2265] 26.31104 35.36324 28.41924 36.14216 35.43929 33.70550 30.39594 24.78749
## [2273] 27.93195 31.27708 26.97068 25.46120 29.96095 31.10800 30.96619 23.30848
## [2281] 26.04352 32.14597 35.15103 30.02151 33.29462 23.75826 23.19855 32.03603
## [2289] 26.47860 34.73126 26.82951 32.01950 27.03453 39.34813 29.41558 34.99371
## [2297] 21.63233 33.57811 30.20280 26.10280 18.32475 30.09742 25.56385 24.92362
## [2305] 28.69942 38.14222 33.99088 27.56321 31.92423 35.85877 28.04404 28.64527
## [2313] 28.01925 38.98666 38.82119 41.37030 28.16129 32.53937 27.91132 19.33952
## [2321] 30.45159 22.52899 32.58788 25.68905 32.55859 20.25457 35.30611 26.32430
## [2329] 37.17110 39.07391 33.86324 30.91852 33.65333 20.30685 34.65364 37.59919
## [2337] 29.42406 28.08843 23.27047 24.85743 28.14748 29.64057 32.18516 28.58887
## [2345] 37.10798 26.47520 36.26003 33.81541 29.38330 20.94701 18.69880 27.08363
## [2353] 35.23756 27.64999 25.87005 21.05545 28.20031 33.24739 19.16920 32.81847
## [2361] 26.72846 33.54111 26.96760 34.16536 27.51467 33.71499 29.62174 32.80621
## [2369] 29.65358 23.64172 30.75631 32.22908 16.43795 27.59380 39.25856 31.46267
## [2377] 25.95258 26.69386 29.17248 27.86869 24.99009 25.52315 27.11339 24.65702
## [2385] 22.30948 32.74530 33.49477 34.73891 31.02584 29.69099 31.50744 28.76059
## [2393] 37.78766 28.68144 33.28031 29.66361 29.56036 38.72601 29.46565 23.41855
## [2401] 37.68921 24.40617 32.66917 34.76240 32.81494 28.56834 29.51347 26.53416
## [2409] 36.21690 27.12328 31.18098 28.80054 29.61740 33.13774 34.87033 21.31599
## [2417] 36.60335 39.25045 26.57333 30.31111 27.79720 26.88667 20.86777 32.37446
## [2425] 29.22742 26.37365 30.47539 19.72587 34.42325 29.12801 29.32406 34.76400
## [2433] 35.51187 22.02726 31.40443 30.41803 26.56911 27.68290 33.31156 27.72603
## [2441] 31.08153 30.27277 29.59897 32.37983 26.11663 33.91167 31.47536 28.08147
## [2449] 23.15429 29.96666 27.73882 24.96725 23.88415 37.32407 34.86439 28.22924
## [2457] 23.43787 29.91357 27.21438 32.41867 31.66782 25.81506 14.87850 22.30028
## [2465] 26.57833 34.94405 28.70648 31.56152 30.47783 16.27746 26.71961 27.59210
## [2473] 19.80421 31.78888 24.98951 31.48849 26.88874 27.63469 22.16530 25.07215
## [2481] 28.13938 27.41855 28.77623 28.55564 24.18087 37.00167 27.13572 27.49027
## [2489] 22.94906 27.98758 35.58583 37.64176 35.28377 34.91600 32.39789 19.90774
## [2497] 31.71787 27.66549 31.06413 29.91794 33.93453 38.26196 24.43428 36.13089
## [2505] 35.92179 31.33688 27.92002 23.65680 27.93207 22.54185 33.67831 29.36807
## [2513] 21.54938 26.77913 22.66206 41.50327 35.13168 25.71123 33.03999 33.31278
## [2521] 37.59640 27.71028 31.19583 29.61022 21.28398 29.21431 30.96455 27.28141
## [2529] 34.41162 32.12894 19.13735 27.61593 18.91502 27.94389 27.39934 28.88297
## [2537] 25.04350 31.40266 24.26926 30.24853 28.60703 29.02351 32.52916 29.74271
## [2545] 21.03924 37.44614 30.11931 32.50096 31.32413 33.82471 26.47086 24.57386
## [2553] 32.15826 34.02282 33.47020 20.24707 30.39035 26.80302 24.96250 26.87354
## [2561] 35.41035 28.43770 23.36349 32.33129 24.69666 24.30461 25.89704 21.07901
## [2569] 35.69890 27.54932 36.33984 33.49758 38.77529 26.60288 29.91882 32.63317
## [2577] 26.52933 36.21761 29.50895 26.64567 31.34122 25.66822 35.29447 29.79487
## [2585] 26.41537 32.20721 36.26013 33.60082 30.55650 26.55687 34.60979 32.91081
## [2593] 30.97133 37.62292 24.51524 32.66278 26.08491 23.49418 32.43857 41.43948
## [2601] 35.99004 38.19333 29.22897 25.25023 22.78441 24.21382 35.50451 22.49891
## [2609] 30.29208 28.82922 27.00261 28.39936 28.80023 25.93391 39.48256 39.59343
## [2617] 31.73127 32.39451 34.77173 29.11668 26.94010 34.43201 27.09563 32.06763
## [2625] 31.63506 28.17182 28.17157 26.49656 23.50922 40.22757 30.32179 31.48994
## [2633] 19.92019 38.72978 32.78599 33.89126 35.16381 39.18928 28.86380 34.05608
## [2641] 25.64868 27.74494 21.84942 27.52994 44.39702 37.90196 37.30746 29.28020
## [2649] 37.46985 27.43866 18.42100 28.95345 27.73019 34.20773 26.91078 23.85734
## [2657] 27.86554 31.21918 24.85613 29.44448 35.39084 27.98449 28.79650 25.97759
## [2665] 39.74326 31.62462 23.38491 25.94255 35.32550 37.10171 39.01768 37.32301
## [2673] 19.74599 31.12415 24.00012 24.59725 30.98944 27.56160 30.50648 30.89006
## [2681] 38.12162 30.86882 24.22259 25.53050 34.47652 37.02084 33.23140 21.11289
## [2689] 25.65867 35.29693 37.58546 24.01701 21.43862 28.68457 25.55975 26.05678
## [2697] 33.23314 30.40345 32.19100 28.18908 39.82610 32.25832 32.35507 25.87723
## [2705] 18.33999 23.66298 25.56252 29.59282 25.78633 26.16917 27.22042 27.84209
## [2713] 24.09089 34.75405 35.53418 25.76709 19.70708 29.59894 34.61537 26.93804
## [2721] 26.87621 36.01603 28.94341 21.21743 33.24339 33.71794 31.17432 36.17122
## [2729] 34.94669 27.76286 15.21363 41.61922 32.88366 26.63190 33.03201 38.62256
## [2737] 27.29488 26.44433 32.02542 31.19134 33.36524 30.94015 31.53913 32.80962
## [2745] 30.27633 33.91534 35.52294 33.80691 26.30533 35.36051 35.86823 31.40437
## [2753] 38.52356 32.19790 31.57217 28.34553 24.23386 33.64881 34.88167 30.94368
## [2761] 23.63331 33.40775 33.84574 22.88119 28.14244 35.18955 33.97979 22.04287
## [2769] 34.17774 45.40956 21.93825 36.53756 24.97741 31.22247 20.37281 39.26104
## [2777] 33.34626 32.23932 36.33348 33.73308 30.62681 31.84998 31.00799 24.37493
## [2785] 26.60283 30.90932 26.29273 20.76072 23.67103 29.07088 33.25686 37.17816
## [2793] 32.75145 33.93059 27.42863 30.76390 29.78532 20.81494 35.11502 28.79113
## [2801] 27.31133 25.66239 21.17667 30.69466 30.03549 31.74621 29.27669 25.45035
## [2809] 34.81795 25.60444 34.92213 38.02980 24.53090 31.32686 39.85295 30.38743
## [2817] 24.08283 33.08592 30.42430 27.36704 13.40415 29.90269 28.06734 34.78432
## [2825] 26.23201 26.44619 25.48226 35.85333 35.83513 24.56401 37.01501 21.61311
## [2833] 35.56198 34.89539 29.75139 24.32647 29.04543 23.58366 25.64932 27.39964
## [2841] 25.84417 36.93378 28.67198 28.56506 38.44486 25.47692 34.10872 31.64576
## [2849] 39.66863 27.49945 31.31161 28.02700 29.31859 23.54422 19.90869 30.58977
## [2857] 29.06316 21.07723 29.31975 26.97502 30.99061 31.39701 33.85001 22.64374
## [2865] 30.38814 25.84552 39.33008 24.21270 36.12821 25.47874 28.70344 33.73805
## [2873] 34.74990 26.61927 31.21992 22.96394 25.21905 37.17006 26.86808 27.69090
## [2881] 20.52221 34.62876 32.91716 39.12414 30.45864 32.82838 22.78636 23.79811
## [2889] 33.62498 31.92221 30.74331 25.80393 26.22572 25.03949 32.54531 30.57111
## [2897] 32.41401 29.57039 25.35558 29.64015 33.25677 24.76371 23.69534 30.16799
## [2905] 42.73682 26.47766 26.55416 29.79205 21.07003 30.73429 33.32318 31.42260
## [2913] 29.06889 24.65169 31.54552 32.81257 29.76744 25.14172 25.80199 30.19792
## [2921] 27.82694 38.40958 35.29921 26.66901 33.56871 28.69799 31.40612 39.28099
## [2929] 32.82179 19.78207 30.35779 30.68354 31.91127 37.43231 21.13197 32.31393
## [2937] 20.16569 38.39008 27.20594 23.89926 28.83929 36.63862 24.97112 36.32322
## [2945] 24.57862 33.57376 26.07368 22.18079 21.16649 27.01833 34.62736 28.97620
## [2953] 36.79522 25.01713 25.94973 35.61587 25.07693 31.96617 31.40111 19.28421
## [2961] 26.43583 27.18903 29.86728 30.42806 32.14376 28.98070 27.50103 24.27654
## [2969] 30.73605 28.53274 29.92477 27.68500 22.73904 32.85130 28.55355 24.09754
## [2977] 25.96220 24.22224 39.55302 34.11378 31.77848 26.90071 39.57272 32.96686
## [2985] 25.42420 24.83012 20.59029 31.67211 31.51085 34.24551 33.51906 32.28413
## [2993] 23.37253 31.63991 31.38001 29.14842 28.73969 31.82755 17.27247 26.05858
## [3001] 30.73073 26.50647 26.42327 36.69433 27.33864 26.28451 34.28066 25.41039
## [3009] 39.93655 29.02741 28.38368 29.21607 23.40179 35.61254 31.31185 30.71437
## [3017] 24.55015 29.55633 38.23731 27.45838 24.87784 28.26731 31.30661 30.97210
## [3025] 22.50116 32.44674 35.22143 37.82424 30.74876 30.09194 31.61575 22.26743
## [3033] 27.79212 32.47881 32.51229 30.19615 27.61575 29.88097 29.23974 27.23248
## [3041] 19.88449 38.01214 39.60186 42.00356 31.00631 34.73246 31.54301 23.38609
## [3049] 31.17411 16.01904 40.41457 32.62514 36.41252 34.11606 34.71504 20.90077
## [3057] 28.50711 31.10036 28.83139 32.19246 22.14794 35.31776 31.60455 24.98838
## [3065] 22.42086 34.20815 28.34809 32.67052 25.49898 34.75014 18.93543 28.51971
## [3073] 25.39406 44.02501 31.87083 29.43267 27.56912 29.21489 38.21086 23.71923
## [3081] 31.03579 27.62285 37.78083 15.54542 26.14693 23.93740 27.45652 27.27338
## [3089] 32.33065 30.02815 43.57375 32.55592 33.44599 32.03989 32.86378 29.98036
## [3097] 36.43065 38.34991 29.55298 25.78564 29.21373 33.85344 27.01380 34.70057
## [3105] 38.90496 31.26781 24.75363 30.35725 30.26948 39.44821 23.89723 20.82040
## [3113] 31.89163 30.36509 31.22574 23.95039 24.76268 30.53732 32.51231 25.37664
## [3121] 33.59199 25.33490 32.44241 34.16648 26.75323 35.20523 26.99766 37.57530
## [3129] 32.75968 28.90261 25.23402 28.56184 38.28637 23.82465 29.68470 19.84116
## [3137] 29.06950 21.18412 26.88744 28.67542 34.73527 25.26832 30.77083 23.34345
## [3145] 24.98246 30.77514 25.42934 34.01041 29.00907 25.76999 28.84973 30.88677
## [3153] 33.70423 33.77929 32.54861 35.80798 37.86933 26.46291 31.29169 31.33040
## [3161] 27.74324 28.95836 37.58213 36.69734 28.62792 19.69640 32.45515 26.21076
## [3169] 30.59901 29.90289 36.71343 35.15721 35.79807 32.12311 29.86151 35.85075
## [3177] 24.17482 30.26760 31.24204 34.24467 21.98944 26.42286 33.24584 32.05453
## [3185] 20.49242 33.78646 29.09921 27.55933 27.84068 30.82428 30.70512 31.84658
## [3193] 31.45758 32.33216 17.40389 29.56404 23.67191 22.06837 33.59279 30.59897
## [3201] 31.00507 28.04585 21.54266 27.93682 31.12089 31.75716 28.27429 25.50711
## [3209] 28.82268 34.78346 21.71231 27.60473 26.77059 33.53834 28.04192 36.25418
## [3217] 25.17146 17.59283 35.60483 28.68012 29.37707 25.50123 28.76966 27.30087
## [3225] 23.07206 20.42349 24.80659 35.82677 23.69139 29.40135 28.49636 28.17960
## [3233] 32.69746 30.46425 34.73899 37.26348 23.23383 21.51366 21.22432 21.31852
## [3241] 30.17902 32.86190 32.54814 26.31984 23.82942 29.18003 31.63074 33.72228
## [3249] 36.17044 32.59527 33.17385 27.26236 22.76853 43.48483 29.14639 32.86033
## [3257] 20.29631 26.02311 31.13066 37.93073 21.14023 34.73664 28.01360 35.59648
## [3265] 28.91842 31.22811 33.67419 33.87248 18.22210 31.58146 17.15258 26.38919
## [3273] 29.02076 30.76993 27.77283 33.74301 27.04652 30.49491 31.15545 17.91077
## [3281] 37.00356 18.63909 29.71123 30.39437 35.79991 27.31516 35.88543 27.25372
## [3289] 27.12095 27.88612 33.02737 28.53378 39.06515 25.93112 33.15441 23.82146
## [3297] 27.00116 24.01967 27.23059 30.12388 32.22435 33.96753 25.97813 27.35273
## [3305] 26.31911 33.62616 32.18924 26.68234 23.96447 25.76889 39.03404 27.13611
## [3313] 31.47611 31.68862 30.14967 34.47830 29.12578 46.27909 26.84659 31.26726
## [3321] 26.37780 36.34058 31.93252 26.61661 21.07192 31.09585 34.13510 35.10806
## [3329] 31.88570 30.86921 31.72292 36.41673 30.35975 27.13167 29.69243 23.95073
## [3337] 26.39326 35.40684 38.52247 39.36463 27.15192 27.97538 25.50707 32.54651
## [3345] 36.88584 22.26215 29.52922 24.64103 31.20787 27.40832 34.78730 31.86699
## [3353] 30.17427 31.39180 40.51884 30.99050 27.73234 30.23615 41.35958 31.08566
## [3361] 37.06942 33.73484 25.37582 38.52440 26.30456 26.92268 34.94529 37.34904
## [3369] 31.83180 29.25480 31.69865 37.09832 32.23266 30.79905 31.72699 36.43691
## [3377] 33.66206 26.34336 28.96996 24.04820 29.11993 29.52836 30.21270 26.53549
## [3385] 43.73900 29.96832 21.69138 27.93648 28.19955 26.28385 31.40393 35.61388
## [3393] 32.09385 26.49771 28.58848 29.12158 41.27780 24.39947 30.33187 33.76045
## [3401] 32.82940 28.54446 26.19916 30.81982 35.86203 33.17955 36.88464 27.69969
## [3409] 31.37921 31.86877 28.62436 27.53602 26.52740 36.27724 30.49303 27.19554
## [3417] 26.68131 29.01782 30.40866 34.73873 29.38284 26.31238 30.09388 35.98493
## [3425] 26.17196 29.34618 25.39514 29.29491 23.25527 30.37078 29.71515 30.55997
## [3433] 35.61343 26.29368 20.93005 37.96600 32.21152 28.50180 28.13886 26.17678
## [3441] 27.66458 22.08698 33.30662 28.39421 35.84227 31.15171 33.44124 27.65586
## [3449] 28.23765 33.48284 37.66156 40.52500 26.96584 21.64974 33.84290 22.84067
## [3457] 32.32416 30.88761 29.00485 31.73252 30.60724 30.26359 34.54384 27.99169
## [3465] 36.14593 33.70396 26.85720 34.21480 27.22034 22.89445 26.64960 26.66669
## [3473] 33.12808 31.00376 21.18148 29.25172 31.07660 31.46224 29.24421 29.76055
## [3481] 27.28232 30.42888 21.15188 26.00527 23.00857 29.96294 30.21941 31.04125
## [3489] 30.49779 26.80776 27.01739 35.60239 25.70467 26.23603 32.93939 39.31799
## [3497] 28.66284 16.29865 40.28316 29.66209 34.99189 32.74287 35.18269 39.88062
## [3505] 34.16850 35.63902 33.10045 25.21558 36.73484 26.62837 22.75642 29.43211
## [3513] 22.50470 20.66226 27.24144 31.49047 32.37230 38.62456 24.64085 26.70080
## [3521] 33.29593 30.57517 16.11968 29.26396 23.86312 31.31092 36.38093 24.79084
## [3529] 33.55359 23.24209 27.36278 28.44040 32.78121 32.32971 25.56036 35.34653
## [3537] 19.41923 27.55155 42.43829 32.53131 34.27470 24.48782 30.20716 26.06133
## [3545] 28.83528 21.34013 27.31595 28.47090 39.81891 26.42465 28.20237 33.11182
## [3553] 41.35214 28.70092 25.62987 35.76791 24.34838 36.44741 33.85161 29.60179
## [3561] 24.57445 24.77740 24.43640 38.06942 28.21902 25.13016 26.24002 28.52797
## [3569] 29.78036 33.74984 33.36733 38.66614 40.20716 30.80145 31.67935 44.39574
## [3577] 34.71213 31.41390 24.78809 32.83015 30.89800 32.65562 32.97760 29.95683
## [3585] 33.40783 19.84971 30.60630 30.32814 33.80837 28.15869 32.79816 32.83991
## [3593] 32.03792 28.22936 25.67252 35.20945 27.66794 23.00947 24.96679 35.05863
## [3601] 25.59183 35.73421 42.04302 21.00242 27.34619 28.90457 33.23161 27.93265
## [3609] 25.83803 36.68567 26.43253 18.15815 24.67209 20.90490 27.50426 25.00554
## [3617] 25.02685 27.53831 22.16316 28.51144 32.20943 24.40314 21.32578 27.97898
## [3625] 24.32225 30.70865 36.44166 33.69955 29.58717 23.17388 33.74887 19.81056
## [3633] 26.67311 32.57997 20.36572 29.56508 30.74156 28.25067 29.34281 27.24569
## [3641] 26.98248 28.48406 32.50014 28.47497 31.88151 30.93222 24.55447 27.92479
## [3649] 24.55625 33.84429 30.99758 30.33359 33.42911 19.34159 22.05469 28.62844
## [3657] 34.32707 37.68048 27.99036 27.56284 31.81198 29.17378 21.89748 34.22026
## [3665] 26.77237 29.13320 37.62613 31.97042 27.95517 24.49629 27.35521 30.86675
## [3673] 28.54674 29.25782 35.59524 41.19055 25.21718 26.58016 32.70963 38.03927
## [3681] 25.41090 28.68019 31.87478 23.48091 26.43997 31.24087 38.41259 25.76300
## [3689] 38.26866 23.65310 28.35961 30.93870 31.65134 31.33093 24.76629 24.44855
## [3697] 29.81043 32.30422 25.75049 39.55146 34.89007 28.98380 28.98066 39.85530
## [3705] 28.92395 36.87402 35.84773 21.31772 30.97571 28.40937 35.26173 37.06986
## [3713] 23.14209 29.30234 31.98059 23.22659 25.24682 32.31686 26.15017 30.14149
## [3721] 29.04566 39.40708 30.29433 28.50168 34.02921 26.97168 23.66388 27.68452
## [3729] 31.41428 32.05304 28.48542 28.70938 25.89472 34.19500 31.09388 23.19824
## [3737] 27.11772 30.88485 27.44318 25.69594 37.13122 32.71243 25.77430 25.37848
## [3745] 32.64458 30.29402 39.57437 32.35120 30.94186 28.33776 32.97784 35.23898
## [3753] 35.64641 30.51706 22.81266 30.90973 34.42729 27.52713 31.95432 28.50752
## [3761] 29.40985 25.84832 41.67597 23.43642 32.88402 31.69156 30.34890 20.98497
## [3769] 36.21497 32.73806 31.21004 31.03604 27.65454 21.82239 21.34416 25.51354
## [3777] 32.38692 34.01295 28.48016 29.98776 39.07833 30.30211 29.93004 25.67835
## [3785] 40.42446 35.04942 36.93824 29.18096 29.99799 34.68340 27.39372 29.99499
## [3793] 37.98130 30.61488 32.43053 30.75400 23.72935 26.91456 17.15273 27.70190
## [3801] 38.54592 24.14751 31.30570 35.88073 26.48355 28.68688 27.36002 36.28140
## [3809] 22.65329 23.19004 26.73634 24.91808 24.12516 34.81460 33.32625 32.62501
## [3817] 19.91885 31.87559 37.78885 27.08005 32.77491 19.54030 29.68319 31.69223
## [3825] 38.25432 31.63927 29.69092 35.20321 28.57330 38.51359 25.68651 25.46621
## [3833] 39.47410 29.77648 34.53371 35.05310 31.32140 29.36863 26.95040 29.94685
## [3841] 31.46263 26.66271 29.93876 31.27741 27.72862 27.95254 29.45579 22.24155
## [3849] 25.49723 39.69048 32.92129 24.08873 22.63891 34.09060 28.00277 30.82548
## [3857] 25.46172 20.95847 28.00776 32.77339 30.87106 36.39276 35.46423 28.06130
## [3865] 32.23515 28.23021 25.61416 30.21564 31.62348 31.11635 25.49296 37.44533
## [3873] 23.63765 23.36803 30.80038 38.98101 30.18916 29.39547 25.81833 27.72943
## [3881] 38.08162 31.99162 35.02148 31.59110 33.31849 44.22908 26.59984 20.65833
## [3889] 21.32567 30.25277 22.32664 38.39192 31.57462 27.91076 29.77226 27.19647
## [3897] 26.20377 39.49991 32.41717 24.62941 31.09961 26.19819 31.56394 35.17670
## [3905] 39.58807 28.12979 34.23232 29.77264 25.12448 35.03822 33.22767 31.82176
## [3913] 30.41447 31.04157 37.55822 35.97870 24.76824 25.17084 35.04353 35.58487
## [3921] 31.77735 29.49184 29.06930 32.79832 22.90022 28.29433 27.24775 33.34307
## [3929] 30.75763 24.36131 24.14437 36.36989 28.43032 29.65834 28.87095 33.25588
## [3937] 40.37865 29.97691 27.13285 30.75794 29.58785 36.13743 35.10361 26.67082
## [3945] 41.29555 40.49196 26.68701 29.75480 35.41742 37.94307 30.50387 30.62858
## [3953] 30.50266 35.55632 28.04648 32.84340 36.83500 33.83080 33.72940 26.91873
## [3961] 27.51917 34.19067 35.42765 38.84467 25.83693 22.97438 39.44776 32.76421
## [3969] 35.67922 36.52037 33.56630 25.56923 26.78776 26.70244 31.92423 27.42323
## [3977] 29.28747 29.56540 35.18943 36.68220 27.22116 32.90449 22.21431 29.30010
## [3985] 26.68967 34.77163 29.33259 28.31328 26.62861 31.34718 29.93272 31.33240
## [3993] 37.02320 33.41958 33.95602 34.01362 30.00906 30.82266 27.70526 26.84066
## [4001] 26.69014 27.49900 31.00239 22.67987 28.64160 37.45084 30.77512 33.15093
## [4009] 29.96366 29.74836 23.86822 21.42214 22.98379 23.20605 27.38748 29.78148
## [4017] 19.93534 32.11370 40.01789 22.79443 36.33678 32.94977 35.52731 32.95445
## [4025] 34.44135 18.56056 35.11807 30.97866 28.53881 24.46769 35.21884 32.79868
## [4033] 21.96948 30.83357 38.20547 25.40861 25.71398 36.62945 22.52032 26.49226
## [4041] 35.44653 22.71253 27.28207 29.59604 36.83558 33.00677 26.81247 21.58151
## [4049] 31.24303 33.42023 24.43196 29.99585 33.06365 31.15957 30.11078 35.21622
## [4057] 43.38493 25.51077 33.88762 24.71156 24.55764 27.18444 28.11999 32.84159
## [4065] 33.26295 28.84270 29.80629 29.09596 37.14773 27.58460 28.37740 32.11482
## [4073] 36.83131 30.83982 36.18205 29.30859 33.57172 25.26525 23.52218 29.29158
## [4081] 35.22407 30.14986 33.15647 26.38986 31.66143 22.43141 26.52966 23.57413
## [4089] 38.24424 23.23537 31.69074 25.01546 26.75264 27.30794 26.72983 29.08023
## [4097] 29.14732 17.35428 34.44553 21.47924 25.17781 36.61121 19.68393 29.57637
## [4105] 39.40361 23.41051 25.86254 28.99337 31.90283 25.93711 20.24536 31.64071
## [4113] 34.73374 33.82240 24.81765 30.94017 32.64282 23.32997 22.98967 33.47638
## [4121] 18.92714 26.37875 28.71852 34.67611 16.98422 24.67271 28.03441 29.16889
## [4129] 35.56191 35.86195 24.31267 31.95533 32.64388 31.44097 29.40248 32.44763
## [4137] 33.83978 28.28105 24.98653 30.06610 32.03605 23.39534 36.67083 31.56801
## [4145] 34.90514 27.61290 35.61476 26.88623 29.55989 20.50363 28.43812 31.98713
## [4153] 25.55469 19.31769 32.37964 29.30280 28.00731 24.19822 22.91748 36.24145
## [4161] 38.85211 28.66385 30.35366 28.94590 28.19737 22.51184 27.87194 29.64855
## [4169] 41.38015 26.75600 32.42307 30.85839 30.50823 25.95655 33.94388 40.59527
## [4177] 27.79192 35.21476 35.00101 31.46405 24.06606 29.68690 30.63144 23.64425
## [4185] 31.96519 36.97733 27.85535 30.62574 32.99732 29.32391 29.58143 22.79570
## [4193] 24.64013 33.42324 34.76386 28.39577 33.62419 28.74767 35.47233 32.83432
## [4201] 18.46405 30.75557 21.77086 32.89475 36.09163 22.41623 26.74553 29.14013
## [4209] 30.17696 34.42833 27.93060 29.61999 23.85636 27.81938 31.73374 28.54607
## [4217] 30.12935 26.82477 22.94356 27.43986 29.28975 26.74853 23.96300 31.84576
## [4225] 36.60969 31.34235 29.49825 28.26917 30.42936 27.75561 22.43813 27.97549
## [4233] 31.41609 35.52977 22.09498 38.36329 27.03481 30.37783 28.12410 26.76093
## [4241] 32.80247 31.80137 34.51802 23.46841 33.60068 30.30910 34.05814 36.18394
## [4249] 23.86574 27.06611 38.37152 22.96306 38.25609 28.60675 39.20669 32.05434
## [4257] 34.34550 32.15331 30.83286 30.27170 25.62649 34.27985 29.81233 28.65501
## [4265] 32.20649 34.13143 30.92788 23.60706 34.85022 28.43662 26.93645 30.78924
## [4273] 33.74842 29.48573 25.82773 39.99977 23.91182 33.98581 30.71605 18.13591
## [4281] 26.85058 31.10091 29.73920 20.52542 24.19601 39.66674 32.76670 36.86146
## [4289] 29.00804 26.49145 24.30740 29.18001 33.73284 30.94657 27.42489 33.76866
## [4297] 34.86931 39.46580 27.00816 22.38927 34.02050 27.21739 26.33981 29.00522
## [4305] 26.16283 32.13944 18.96335 28.34547 26.91684 38.56974 36.97570 30.35776
## [4313] 29.25064 26.86842 32.02204 25.17937 38.62327 30.32375 34.04721 23.19600
## [4321] 39.62852 30.60867 27.01563 22.10722 27.95725 22.97513 24.37781 28.18870
## [4329] 20.59349 25.08522 25.13508 24.22048 24.07759 25.40863 24.38443 34.67268
## [4337] 26.47462 31.36538 28.24219 26.78769 25.58259 28.69178 30.57724 34.71546
## [4345] 33.60022 33.11751 31.88312 28.26882 29.43477 39.56930 27.33604 26.56342
## [4353] 25.76371 21.31298 31.30834 28.57673 31.14224 20.87590 32.29596 36.06565
## [4361] 27.68453 38.88812 32.57034 20.84170 37.05761 33.25884 28.35397 27.84843
## [4369] 30.27615 31.57369 23.13815 28.67886 28.26385 31.49044 21.96185 19.99215
## [4377] 23.34592 32.77787 27.04701 24.27666 25.61861 30.76315 26.67764 34.46869
## [4385] 29.23152 22.26946 26.67746 27.83651 35.27964 27.77226 36.19924 34.29250
## [4393] 27.73053 29.23994 33.79430 39.96940 24.30654 30.87573 29.83303 28.18121
## [4401] 26.90553 36.38206 37.54684 21.51075 23.67336 29.29114 31.00925 29.42763
## [4409] 32.15519 33.99389 30.14386 33.75912 34.98433 24.69119 32.69998 30.79248
## [4417] 35.50974 29.10640 33.33173 38.80145 25.45860 32.98971 35.27276 22.15320
## [4425] 31.37908 27.83751 29.70155 34.98005 27.04623 31.86302 30.56944 30.25525
## [4433] 33.08488 24.29545 32.13056 28.88996 22.93656 22.90671 33.77146 34.18213
## [4441] 32.96572 37.43502 31.07117 37.09059 27.23155 37.06707 24.07597 32.01888
## [4449] 34.93151 28.84225 27.54381 26.22446 26.80151 28.87877 34.35873 30.30683
## [4457] 27.59402 26.49132 36.76228 32.38950 23.98371 26.84195 35.87177 38.99896
## [4465] 31.22588 26.97051 31.23316 38.41349 22.41242 27.88017 31.09794 40.99217
## [4473] 28.02196 34.00079 34.20589 32.44751 38.89426 26.86787 28.75191 26.86484
## [4481] 25.02624 31.65766 26.64438 37.75789 34.02121 30.96946 39.40545 27.77702
## [4489] 26.31017 30.48953 26.31616 30.44566 30.18662 29.00653 29.11527 35.67581
## [4497] 31.51718 27.79081 26.83737 31.64891 20.64285 33.43513 30.62705 35.31666
## [4505] 29.19225 21.77999 23.20130 24.88608 32.82345 29.94227 29.64197 29.96027
## [4513] 28.19084 32.02919 31.93120 38.29088 35.74358 26.12004 29.46827 31.22700
## [4521] 31.11326 25.05748 32.78559 30.84627 33.00452 33.83732 24.78598 24.32742
## [4529] 32.59257 31.21209 30.94147 27.59922 35.79510 34.34188 30.45735 33.18959
## [4537] 25.36764 21.71455 25.19171 27.94759 29.38884 49.51812 37.40484 37.63207
## [4545] 34.77620 24.20404 34.78328 39.88484 34.57993 22.26946 31.38175 27.64634
## [4553] 30.19248 22.63627 27.95068 25.82023 34.93184 23.84620 26.29097 22.94240
## [4561] 31.82086 30.77031 28.76898 32.23850 25.56477 23.35790 29.65412 33.80786
## [4569] 39.67616 32.44777 26.59982 30.16611 35.50782 23.54488 24.42507 21.98266
## [4577] 30.04015 37.46662 29.53798 34.51594 39.26410 35.35798 38.68489 30.26612
## [4585] 32.17502 30.20054 29.09998 24.31146 36.74270 27.12958 33.79153 25.40962
## [4593] 26.07072 39.59025 25.68191 37.30465 25.38823 26.44938 24.20349 27.59418
## [4601] 36.17295 30.80188 23.16196 30.26740 35.87703 24.65028 28.54728 30.00725
## [4609] 46.85717 30.17218 37.76566 31.76757 25.51225 25.00761 35.21354 27.25501
## [4617] 30.36619 31.29513 28.02949 29.07942 25.91787 32.06208 25.73639 39.27906
## [4625] 22.14061 29.14861 36.10753 35.97249 31.56338 32.40164 30.67781 28.77315
## [4633] 26.84231 31.71392 30.58271 26.87784 33.18633 29.07927 28.43277 34.63518
## [4641] 42.79660 30.67926 23.41599 35.39429 25.84704 31.43060 30.09875 34.06124
## [4649] 24.25024 33.04293 34.82711 25.85508 23.42945 32.75616 32.27380 29.20109
## [4657] 35.19657 33.15573 36.46191 19.39558 32.58884 22.17815 19.06440 29.76962
## [4665] 33.09396 26.00538 37.00354 23.44167 28.82748 25.88845 32.48944 26.94580
## [4673] 18.62812 25.46511 22.94801 26.05915 30.37081 28.54672 36.02573 30.30231
## [4681] 30.31465 20.82602 32.20043 33.19629 32.82036 31.92148 31.22729 29.58644
## [4689] 36.24159 15.75385 27.17060 30.14181 23.25469 41.28542 28.13571 37.84658
## [4697] 26.62060 30.20938 33.73791 30.39899 37.96609 35.61591 25.97872 23.36457
## [4705] 32.74230 27.44864 35.23041 28.54012 30.22458 25.41220 31.06779 39.90915
## [4713] 30.06417 26.86189 27.31390 34.72874 29.36311 40.24147 34.89909 27.40600
## [4721] 30.77753 34.16257 29.62351 32.08122 26.87426 28.23376 35.50586 23.48043
## [4729] 27.13938 45.37310 24.32181 24.41967 28.90946 33.76102 32.35397 30.92802
## [4737] 36.16524 29.76250 33.89681 22.95552 29.37452 30.97203 37.36333 30.63461
## [4745] 28.54170 22.59288 32.57748 27.72039 24.33850 29.21769 22.89880 30.38653
## [4753] 20.90407 30.57685 29.69113 26.33786 31.52466 22.09867 33.37876 29.71305
## [4761] 40.10389 27.08785 30.16009 31.68072 31.24625 33.80256 29.57066 33.15768
## [4769] 26.65357 20.31061 27.85921 31.54872 21.22955 39.10236 25.43812 24.23564
## [4777] 34.35876 31.79971 33.87243 24.67916 32.35363 33.34903 27.45211 30.72729
## [4785] 21.11120 26.21764 36.15043 35.62117 31.56191 25.20283 25.52326 31.00241
## [4793] 31.49477 32.89769 23.74794 37.92798 24.64802 25.98263 34.30432 36.67548
## [4801] 37.05652 34.16603 29.57609 28.87177 28.05345 21.14603 32.43175 33.30936
## [4809] 37.54476 36.37637 33.82748 33.03615 24.07290 31.42836 24.71322 31.53942
## [4817] 29.66540 30.48004 34.09528 37.03555 40.91400 30.58757 39.38940 36.23409
## [4825] 27.26948 35.62552 25.27165 29.57868 28.12030 27.44148 32.18363 27.01100
## [4833] 31.79671 29.92215 30.09550 24.55465 27.48469 27.82900 27.15368 27.73149
## [4841] 28.02643 31.40064 34.02211 35.01131 34.03490 32.57506 41.64070 25.89611
## [4849] 30.62390 36.94750 26.78646 25.50790 32.96594 36.36024 27.76356 31.04529
## [4857] 30.74692 25.72400 26.47032 41.23620 23.07089 33.91900 35.13848 25.83311
## [4865] 24.96004 30.46329 33.31925 21.42036 31.10711 34.39120 28.28021 35.17607
## [4873] 29.94213 33.30404 32.29632 25.64228 26.66725 30.87406 26.42299 38.94620
## [4881] 28.51089 24.55310 25.62605 29.04915 32.19367 22.68246 22.26558 26.26156
## [4889] 22.25948 31.65918 29.72623 29.10419 31.50860 31.40636 45.14762 31.77800
## [4897] 30.25172 22.97833 36.17168 27.06940 33.36810 36.63372 37.72105 28.54003
## [4905] 31.39679 25.08252 31.14438 26.01840 34.52786 29.15456 35.57742 33.05487
## [4913] 33.62725 26.01421 26.49855 25.82092 30.45149 28.11672 44.67474 19.96126
## [4921] 23.42012 28.67253 31.57582 22.02577 31.47005 27.75224 26.78911 20.37561
## [4929] 29.11888 30.88027 41.33138 37.37297 29.10156 31.00639 33.78860 28.24316
## [4937] 36.58601 27.26951 31.30554 32.60899 29.80450 34.02610 33.29567 24.20215
## [4945] 31.55609 29.88506 36.55797 25.57416 35.30472 32.42507 32.86773 28.57240
## [4953] 26.76590 35.80690 32.71019 34.08037 27.82001 32.26160 26.77035 32.94493
## [4961] 26.03002 32.53625 34.54233 28.03073 26.12284 28.77127 36.29112 24.33292
## [4969] 34.79282 37.22609 27.23402 31.42153 26.13276 37.30459 24.45224 26.11242
## [4977] 33.13941 30.77142 30.02384 35.09638 39.43497 26.64872 34.47223 34.46085
## [4985] 27.77859 30.27080 29.21942 32.19390 30.77374 33.18021 27.40355 20.87694
## [4993] 27.24607 37.88885 27.06450 27.08537 34.70258 25.41097 32.37093 33.40900hist(life_time, main = "Distribución de tickets en promedio", col = "blue")
prop_supera_35 <- mean(life_time > 35)
prop_supera_35## [1] 0.1598Conclusión
Los tiempos de atención siguen una distribución aproximadamente normal centrada en 30 minutos; alrededor de un tercio de los casos superan los 35 minutos, lo que refleja la variabilidad natural en el proceso.
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Punto 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(0731)
test <- rbinom(1000, 10, 0.20)
test## [1] 3 3 1 2 2 3 3 3 2 0 1 1 3 3 1 3 3 1 5 1 3 3 2 3 3 2 1 1 2 3 0 1 0 3 5 1 2
## [38] 1 2 0 1 2 1 2 1 0 1 0 3 2 1 2 4 3 3 2 3 3 1 4 3 1 2 2 3 1 0 2 2 2 1 2 2 1
## [75] 0 3 1 3 2 2 2 1 3 1 4 4 2 0 0 2 0 1 3 2 2 1 0 1 4 2 0 0 6 4 2 3 1 2 4 2 3
## [112] 2 4 1 3 2 3 0 0 0 1 2 5 3 2 2 2 1 1 1 3 3 3 2 3 2 3 4 0 2 3 4 2 1 0 3 2 2
## [149] 2 5 3 4 1 1 2 2 1 3 1 7 2 2 2 2 0 2 1 3 0 0 2 2 0 2 1 1 4 2 2 2 0 3 2 2 1
## [186] 4 3 1 3 0 2 4 5 0 1 2 0 0 2 2 2 4 1 3 1 0 0 2 2 0 1 2 2 3 2 1 1 2 3 2 4 0
## [223] 1 2 4 0 2 0 4 0 1 0 1 2 1 0 1 3 4 1 3 2 2 1 3 2 2 2 3 1 2 3 1 3 1 2 3 2 3
## [260] 1 2 2 2 3 0 1 4 3 3 2 1 3 2 0 1 2 4 2 4 1 3 2 2 2 4 2 3 2 2 2 0 3 3 0 2 2
## [297] 3 2 1 3 3 2 2 1 3 2 1 1 1 2 1 5 2 2 3 2 1 1 4 1 3 0 3 1 1 0 1 2 0 1 3 0 1
## [334] 2 1 3 0 1 1 2 1 5 2 2 3 3 2 3 2 1 0 4 0 3 0 1 1 3 2 4 1 3 5 2 4 2 3 2 3 3
## [371] 4 1 5 4 2 1 4 1 2 3 2 2 1 3 0 2 2 2 3 0 2 1 1 3 1 2 3 3 2 5 4 0 2 4 3 3 0
## [408] 4 2 2 1 2 6 3 1 2 0 1 3 0 1 2 2 2 3 2 1 5 0 1 2 2 1 2 2 1 3 2 2 3 2 1 3 3
## [445] 2 2 2 2 1 1 2 3 3 4 2 0 2 1 2 3 2 2 3 5 2 0 4 0 3 4 1 2 1 2 3 1 1 2 1 3 1
## [482] 1 2 0 1 2 2 3 3 3 4 4 2 1 3 2 5 2 1 1 0 0 4 1 3 2 1 3 2 5 1 2 2 3 2 1 1 0
## [519] 0 2 4 3 5 3 1 2 3 0 0 2 0 1 2 0 1 0 3 1 2 3 2 2 2 2 1 3 3 3 1 2 2 3 1 2 1
## [556] 4 0 2 1 2 2 1 1 4 3 2 0 0 2 2 2 2 0 1 0 2 2 2 2 1 1 0 1 3 1 2 3 2 3 1 2 1
## [593] 3 2 5 2 1 1 3 0 1 1 2 2 2 2 2 1 2 4 0 1 2 1 6 2 2 2 1 2 1 2 2 1 5 1 0 1 3
## [630] 2 1 2 0 1 4 1 4 2 2 3 2 4 3 4 3 2 1 1 1 1 3 4 0 1 2 4 3 2 1 2 3 2 2 3 1 0
## [667] 1 1 0 3 1 3 3 4 2 2 3 1 3 2 1 3 3 0 2 2 1 3 3 0 0 2 2 3 0 2 1 2 0 6 1 1 8
## [704] 3 2 4 2 0 5 5 3 2 1 1 3 2 2 3 1 3 5 1 4 1 1 0 1 3 3 3 1 3 3 1 5 3 3 2 1 4
## [741] 3 1 2 1 2 2 2 4 2 2 2 4 1 3 0 3 1 1 1 2 1 3 0 4 3 1 1 2 2 1 1 1 3 2 2 2 0
## [778] 2 2 0 2 3 1 3 2 3 2 0 0 2 0 0 2 3 2 3 1 3 1 0 0 5 1 4 3 3 1 1 1 2 1 2 2 2
## [815] 1 4 2 2 1 1 1 1 1 3 1 1 2 1 2 1 3 1 3 3 1 2 2 1 2 3 0 1 3 3 4 4 2 1 1 0 1
## [852] 2 3 2 3 2 4 3 1 0 2 1 1 2 3 1 3 0 5 0 0 2 2 2 0 0 2 4 1 3 0 3 2 3 2 2 4 2
## [889] 1 2 4 2 4 1 2 1 2 1 2 2 3 1 2 2 0 1 1 3 1 2 1 1 4 4 2 3 1 3 0 1 0 1 1 2 2
## [926] 1 1 1 3 3 2 0 2 1 4 0 2 1 1 1 1 2 1 0 1 1 1 2 3 1 4 0 1 3 2 1 1 1 2 1 0 2
## [963] 2 2 1 2 0 4 2 4 3 2 3 0 1 2 1 1 3 1 1 3 1 1 3 2 2 2 2 4 3 2 2 2 2 3 1 2 5
## [1000] 0total_escalados <- sum(test)
total_escalados## [1] 1941hist(test, main="Distribucion Tickets escalados a segundo nivel ", col = "Green")
freq <- table(test)
barplot(freq,
main = "Tickets escalados a segundo nivel",
col = "green",
xlab = "Tickets escalados en una hora",
ylab = "Frecuencia en 1000 horas")
Conclusión
a simulación muestra que, en promedio, se escalan cerca de 2 tickets por hora al segundo nivel, con variaciones alrededor de ese valor, lo que coincide con la probabilidad teórica del 20%.