Utilizando la distribuición normal
Teniendo en cuenta una población de media 30 y varianza 36.
- Calcular la probabilidad de que X sea menor o igual a 20
\[ P(X\leq 20) \]
pnorm(20, mean = 30, sd = sqrt(36))## [1] 0.04779035- Calcular la probabilidad de que X se encuentre entre el 25 y 27
pnorm(27,30,6) - pnorm(25,30,6)## [1] 0.1062092- Valor de X que deja un 80% por debajo de el \[ P(X\leq x_0)=0.80 \]
qnorm(0.80, mean = 30, sd= 6)## [1] 35.04973- Genera un conjunto de datos de 100 con la misma media y varianza
rnorm(100, mean=30, sd= 6)## [1] 24.26825 24.32165 39.58960 29.57013 27.88652 27.02064 30.51561 29.12012
## [9] 29.40190 29.22589 34.39514 22.16782 23.70240 34.03841 25.33633 30.17439
## [17] 23.57894 25.79928 25.89958 27.99958 28.38460 26.99130 21.22613 32.46164
## [25] 25.53592 30.83114 37.65733 37.26820 29.28290 22.60692 27.45457 30.30036
## [33] 39.70108 27.03516 27.86495 36.74418 29.93081 41.08182 34.67799 37.23019
## [41] 25.04859 31.67653 23.48794 27.78678 26.94986 31.11482 35.59182 24.45375
## [49] 20.48141 29.46355 24.59540 28.60668 29.45330 39.05911 21.68058 26.76726
## [57] 37.31745 36.09069 27.42673 33.71649 24.41060 22.09118 16.56837 27.99372
## [65] 29.36282 28.03104 38.75500 32.95993 24.23380 30.75508 28.11243 32.17097
## [73] 26.43164 32.14330 28.02780 36.98360 22.63552 34.82084 24.63697 15.53863
## [81] 33.90872 28.77839 19.10057 28.73296 33.56678 29.85898 24.11299 25.87626
## [89] 31.29748 25.65326 32.84102 31.87216 31.74460 24.03346 39.69165 31.10562
## [97] 42.85325 36.18748 19.71926 33.01819- Construya una campana de Gauss para los datos
curve(dnorm(x, mean=30, sd= sqrt(36)), xlim = c(10,45), xlab="Valores de x", ylab= "Densidad de X")