Question

A survey found that​ women's heights are normally distributed with mean

63.8

in. and standard deviation

3.1

in. The survey also found that​ men's heights are normally distributed with mean

69.4

in. and standard deviation

3.8

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

56

in. and a maximum of

62

in. Complete parts​ (a) and​ (b) below.

If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements? The new height requirements are a minimum of nothing in. and a maximum of nothing in.

Answer 1

It is given that the survey found that​ men's heights are normally distributed with mean 69.4 in. and standard deviation 3.8 in.

So .

The tallest​ 50% of men represents the mean (median) of the normal distribution.

So

The shortest​ 5% of​ men (5th percentile) is such that

The new height requirements are a minimum of 63.15 in. and a maximum of 69.4 in.