Question

Find the following probabilities for the standard normal distribution in R or using the standard normal table. Note I always recommend drawing the distribution. (Round your answers to four decimal places) ### Example R code mu-o: sigma = 1: x = x; # Note you will have to change the value of x. pnorm(x,mu.sigma) (a) PIX s 0.41) (b) P(X 2041) () PIXs-4.25) Find the following percentiles for the standard normal distribution in Ror using the standard normal table. (Round your answers to two decimal places.) a Example R code mu-o, sigma . 1; p . P; # Note you will have to change the value of p. gnormip.mu,sigma) (a) 81st (b) 19th (c) 74th

Answer 1

(a)

P(X $\le$ 0.41) =  0.6591

Run the below code in R studio

mu = 0; sigma = 1; x = 0.41
pnorm(x, mu, sigma)

(b)

P(X $\ge$ 0.41) =  0.3409

Run the below code in R studio

mu = 0; sigma = 1; x = 0.41
pnorm(x, mu, sigma, lower.tail = FALSE)

(c)

P(X $\le$ -4.25) =  0.00001

Run the below code in R studio

mu = 0; sigma = 1; x = -4.25
pnorm(x, mu, sigma)

(a)

81st =   0.88

Run the below code in R studio

mu = 0; sigma = 1; p = 0.81
qnorm(p, mu, sigma)

(b)

19th = -0.88

Run the below code in R studio

mu = 0; sigma = 1; p = 0.19
qnorm(p, mu, sigma)

(c)

74th =   0.64

Run the below code in R studio

mu = 0; sigma = 1; p = 0.74
qnorm(p, mu, sigma)

Answer 2

mu = 0; sigma = 1; x = 0.41
pnorm(x, mu, sigma)