Let X be a normally distributed random variable with mean µ = 20 and standard deviation σ = 10. Find x ∗ satisfying each. (a) P(X < x∗ ) = 0.73 (b) P(X > x∗ ) = 0.59

Answer 1

use standard z-score formula z = (x - mean)/SD = (x = 20)/10 for this problem.

a) find z-score for 0.73, approximately 0.64, so,

0.64 = (x-20)/10

x = 26.4

b) if P(X > x*) = 0.59

then P(X < x*) = 0.41

find z-score for 0.41, approximately -0.23, so

-0.23 = (x-20)/10

x = 17.7