Question

Assume that women's heights are normally distributed with a mean of 45.7 inches and a standard deviation of 2.25 inches. If 900 women are randomly selected, find the probability that they have a mean height between 45 inches and 45.6 inches.

Answer 1

Given,

= 45.7 , = 2.25

Using central limit theorem,

P( < x) = P( Z < x - / ( / sqrt(n) ) )

P( 45 < < 45.6) = P( < 45.6) - P( < 45)

= P( Z < 45.6 - 45.7 / 2.25 / sqrt(900) - P( Z < 45 - 45.7 / 2.25 / sqrt(900)

= P( Z < -1.3333) - P( Z < -9.3333)

= 0.0912 - 0

= 0.0912