Normal Distribution

Question

A sample of size 36 is drawn from a population with mean 47 and standard deviation of 9. Find P (X ≤ 47.9)

Answer 1

X is N(47,9)

to find P(x <= 47.9) we are going to transform that inequality to N(0,1) using z-stat = (x - mean)/SD = (x - 47)/9:

P(x < 47.9) = P(z < (47.9 - 47)/9) = P(z < 0.1) = 0.5398