The hieght,X ,of young American women is distributed normal with mean 65.5 and standard deviation 2.5 inches .find the probability of each the following events.

Question

a- X<67
b-64<X<67

Answer 1

1. find
Z-score = (X-mean)/stdev
=(67-65.5)/(2.5)
=(1.5)/2.5
=0.6
2. Look up standard normal distribution tables for one-tail where Z-score = 0.6
P(x<X=67)=0.7257469 [from tables for Z=0.6]

For part b, find similarly P(x<X=64)
then
P(64<x<67)
=P(x<67)-P(x<64)