Question

Assume that women's heights are normally distributed with a mean given by , and a standard deviation given by . μ = 63.5 in σ = 2.8 in (a) if 1 woman is randomly selected, find the probability that her height is less than 64 in. (b) if 33 women are randomly selected, find the probability that they have a mean height less than 64 in.

Answer 1

 (a) if 1 woman is randomly selected, find the probability that her height is less than 64 in
using z-score formula:
z-score=(x-mu)/sig
(64-63.5)/2.8
=0.18
thus
P(x<64)=P(z<0.18)-=0.5714

B]  if 33 women are randomly selected, find the probability that they have a mean height less than 64 in
using the central limit theorem of sample means, we shall have:
2.8/√33=0.49
since n>30 we use z-distribtuion
z(64)=(64-63.5)/0.49=1.191
The
P(x_bar<64)=P(x<1.191)=0.8830