Question

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value x 0of the random variable x. (Round to two decimal places as needed.)

p(x >x 0): 0.95

Answer 1

Note that:

If, X ~ Normal , then,

We have to use software or Standard Normal table to find its value, I will use R studio here.

R code: pnorm(z)

Also let, , kth quantile of N(0,1)

R code: qnorm(k)

Here, X ~ Normal()

So,

R output:

 > qnorm(0.05) [1] -1.644854