Calculando probabilidades com o R

Distribuição Normal X ~ N(50,30)

a) Pr(X < 50):

prob_a <- pnorm(50, mean = 50, sd = 30)
prob_a
## [1] 0.5

b) Pr(40 < X < 61):

prob_b <- pnorm(61, mean = 50, sd = 30) - pnorm(40, mean = 50, sd = 30)
prob_b
## [1] 0.2736248

c) Pr(33 < X < 47):

prob_c <- pnorm(47, mean = 50, sd = 30) - pnorm(33, mean = 50, sd = 30)
prob_c
## [1] 0.1747018

Distribuição Normal Y ~ N(10,15)

a) Pr(5 < Y < 7):

prob_d <- pnorm(7, mean = 10, sd = 15) - pnorm(5, mean = 10, sd = 15)
prob_d
## [1] 0.05129895

b) Pr(9.5 < Y < 11):

prob_e <- pnorm(11, mean = 10, sd = 15) - pnorm(9.5, mean = 10, sd = 15)
prob_e
## [1] 0.03987208

c) Pr(Y > 7.5):

prob_f <- 1 - pnorm(7.5, mean = 10, sd = 15)
prob_f
## [1] 0.5661838