Objetivos Simular una muestra aleatoria conforme a la distribución normal con la función rnorml() de media igual a 175 y desviación std de 6, demostrar la lejanía de los datos con respecto a la media Demostrar que las probabilidades de los siguientes intérvalos en la muestra simulada se a proximan a los valores siguientes p(μ−1σ<x<μ+1σ)≈0.6827 p(μ−2σ<x<μ+2σ)≈0.9545 p(μ−3σ<x<μ+3σ)≈0.9973

set.seed(2020)
estaturas= round(rnorm(300,175,6),4)
estaturas
##   [1] 177.2618 176.8093 168.4119 168.2176 158.2208 179.3234 180.6347 173.6237
##   [9] 185.5548 175.7042 169.8813 180.4556 182.1782 172.7705 174.2604 185.8003
##  [17] 185.2240 156.7674 161.2662 175.3498 188.0462 181.5891 176.9093 174.5611
##  [25] 180.0056 176.1925 182.7870 180.6203 174.1154 175.6626 170.1250 170.5378
##  [33] 181.5721 189.6122 177.3287 176.7438 173.2864 175.4561 171.6382 177.6831
##  [41] 180.4510 171.9696 173.1940 170.6438 167.9195 176.5184 172.7757 175.1331
##  [49] 178.9603 177.9328 173.8673 178.6082 170.9574 177.8563 175.7125 175.7274
##  [57] 173.8837 167.0304 171.5985 178.4730 186.4542 176.5045 165.4101 194.2098
##  [65] 180.7314 177.2119 180.5375 173.7669 175.5578 176.0096 179.7750 184.8760
##  [73] 164.6985 173.0899 169.5752 170.7760 164.3314 170.6665 175.2769 176.4619
##  [81] 178.7700 174.8522 188.8849 176.0633 168.8535 188.6481 163.6657 181.5637
##  [89] 186.0770 178.1262 165.8022 163.3638 177.9215 182.4714 173.6964 170.3224
##  [97] 177.0932 179.0903 171.8112 170.9356 164.6273 169.0524 171.4870 177.3011
## [105] 179.4800 169.4295 172.9709 184.2707 176.5991 176.7972 173.0632 183.6121
## [113] 181.0392 164.6835 176.7935 170.0516 167.8025 167.3417 174.2609 187.9957
## [121] 173.1263 177.2046 182.6166 161.4109 167.2609 176.1273 179.5099 185.7081
## [129] 184.0496 169.2810 175.6205 171.3666 174.4144 174.2593 168.7319 174.5508
## [137] 185.5608 166.4073 190.9732 167.2529 175.0906 174.7619 188.1486 163.1414
## [145] 177.7820 173.4267 168.1857 176.2678 175.5966 156.6599 172.9172 163.3202
## [153] 173.7035 166.3048 177.0726 176.1292 168.2329 175.3027 170.9038 178.8883
## [161] 178.6622 171.9241 179.5264 176.1286 163.4303 182.4149 176.9697 169.8705
## [169] 163.6259 180.0802 182.4642 176.4176 170.4358 179.6333 178.9693 165.4376
## [177] 161.8579 167.9395 181.3000 174.9658 173.3439 180.0911 168.7064 164.5985
## [185] 189.4848 173.8261 180.5607 170.7192 167.2015 180.3058 182.2038 167.9780
## [193] 179.5688 180.2205 170.6365 178.7597 168.4513 171.9034 175.1016 178.9659
## [201] 170.6228 180.1083 172.6211 177.4401 168.7687 167.4647 181.9421 181.2321
## [209] 174.4286 168.4102 178.3621 173.4818 188.2426 170.5417 177.6782 175.6342
## [217] 168.8792 180.5438 168.3649 171.7375 178.3860 166.5996 174.1585 174.1343
## [225] 170.3919 178.8295 181.7123 177.6752 163.5510 174.9161 178.0379 177.7021
## [233] 165.0249 185.0189 159.3615 179.7854 177.9201 179.0761 175.8302 185.1699
## [241] 175.2667 175.1912 190.2187 184.5759 175.7951 173.4971 162.9528 183.8027
## [249] 173.0313 170.2328 174.9882 171.3645 184.2599 168.2186 167.3861 170.7101
## [257] 182.4640 175.9158 177.8732 179.7172 168.9135 165.0432 173.8243 178.3633
## [265] 174.0413 166.8480 165.9793 174.4163 180.8036 173.1919 160.5087 167.6455
## [273] 171.2505 169.1461 160.6797 188.4015 180.3511 176.3151 169.9315 166.8320
## [281] 175.8872 158.3401 179.5468 170.1096 181.3014 172.6448 175.0633 180.8953
## [289] 180.2923 162.2170 156.3297 171.2995 182.5510 173.6360 176.9456 170.8533
## [297] 171.8709 185.9319 169.2995 171.5563

Diagramas de visualización de datos Dispersión

plot(estaturas)

Histograma

hist(estaturas)

Boxplot

boxplot(estaturas)

Estadistica:

n= length(estaturas)
m=mean(estaturas)
std=sd(estaturas)
n
## [1] 300
m
## [1] 174.7075
std
## [1] 6.817341

Cerca de un 68% de las veces una variable aleatoria normal toma un valor dentro de una desviación estándar

lin= m-1 * std
lsu= m+1 * std


plotDist(dist = "norm", mean=m, sd=std, groups=  x>lin & x<lsu  ,type = "h")

pnorm(q=lsu,mean=m,sd=std) - pnorm(lin,m,std)
## [1] 0.6826895

cerca del 95% de las veces el valor se encuentra dentro de dos desviaciones estandar de la media

lin=m-(std*2)
lsu=m+(std*2)
plotDist(dist = "norm", mean=m, sd=std, groups=  x>lin & x<lsu  ,type = "h")

pnorm(q=lsu,mean=m,sd=std) - pnorm(lin,m,std)
## [1] 0.9544997

cerca del 99% de las veces, una variable aleatoria está dentro de 3 desviaciones estándar

lin=m-(std*3)
lsu=m+(std*3)
plotDist(dist = "norm", mean=m, sd=std, groups=  x>lin & x<lsu  ,type = "h")

pnorm(q=lsu,mean=m,sd=std) - pnorm(lin,m,std)
## [1] 0.9973002