Question

A survey found that women's heights are normally distributed with mean 62.8 inches and standard deviation of 2.5 inches. This survey also found that men's heights are normally distributed with a mean 67.7 and a standard deviation 2.8.
A. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in and maximum of 6 ft 2 in. Find the percentage of women meeting height requirements. __%

B. Find the percentage of men meeting the height requirements. __%

C. If height requirements are changed to exclude only the tallest 5% of men & the shortest 5%, what are the height requirements?

The new height requirements are at least __in and at most__in.

Answer 1

Hello there.

A survey found that women's heights are normally distributed with mean 62.8 inches and standard deviation of 2.5 inches. This survey also found that men's heights are normally distributed with a mean 67.7 and a standard deviation 2.8. 

A. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in and maximum of 6 ft 2 in. Find the percentage of women meeting height requirements. __%

Answer 2

a) 

Z*_Upper = (76 - 62.7)/2.5 = 5.32

Z*_Lower = (57 - 62.7)/2.5 = -2.28 

The requirement is to get p(-2.28 < Z < 5.32) = p(Z<5.32) - p(Z<-2.28). 

Use normal distribution table to get the answer for p and multiply with 100 to get the percentage. 

The other questions are now easy for you to answer on your own. Hope it helps.