Question

The mean height of women in a country​ (ages 20minus ​29) is 63.6 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 ​inches? Assume sigma equals2.84 . The probability that the mean height for the sample is greater than 64 inches is

Answer 1

Given,

Mean = = 63.6 inches

Standard deviation = = 2.84 inches

Sample size = n = 60

According to the Central Limit Theorem.

Let Z = (X - ) /( /sqrt(n)) is a standard normal random variable.

P(X > 64) =P((X - ​​​​​​) /(/sqrt(n)) > (64 -) /(/sqrt(n)))

P( X > 64) = P( Z > (64 - 63.6)/(2.84/sqrt(60)))

P(X > 64)= P(Z > 1.09)

P(X > 64) = 1 - P( Z < 1.09)

P( X > 64) = 1 - 0.8621

P(X > 64) = 0.1379

The probability that the mean height for the sample is greater than 64 inches is 0.1379