Find the following probabilities for the standard normal distribution in R or us

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-0; sigma-1; x-x; # Note you will have to change the value of x. pnorm(x,mu,sigma) (a) P(X S 0.79) (b) P(X 2 0.79) (c) P(X s -3.84) Find the following percentiles for the standard normal distribution in R or using the standard normal table. (Round your answers to two decimal places.) # # # Example R code mu-0; sigma-1; p-p; # Note you will have to change the value of p. qnorm(p,mu,sigma) (a) 61st (b) 39th (c) 75th

Explanation / Answer

1)

> mu=0
> sigma=1

#P(X<0.79)
> pnorm(0.79, mu, sigma)
[1] 0.7852361

#P(X>0.79)
> 1-pnorm(0.79, mu, sigma)
[1] 0.2147639

#P(X<-3.84)
> pnorm(-3.84, mu, sigma)
[1] 6.151716e-05

2)

> mu=0
> sigma=1
#p= 0.61 or 61 st percetile
> qnorm(0.61,mu,sigma)
[1] 0.279319

#p= 0.39 or 39 st percetile
> qnorm(0.39,mu, sigma)
[1] -0.279319

#p= 0.75 or 75 st percetile
> qnorm(0.75, mu, sigma)
[1] 0.6744898

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