Question

A survey found that​ women's heights are normally distributed with mean 62.6 in. and standard deviation 2.6 in. The survey also found that​ men's heights are normally distributed with a mean 67.6 in. and standard deviation 2.7. Complete parts a through c below.

a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 3 in. Find the percentage of women meeting the height requirement.

The percentage of women who meet the height requirement is__​%.

​(Round to two decimal places as​ needed.)

b. Find the percentage of men meeting the height requirement.

The percentage of men who meet the height requirement is__%.

​(Round to two decimal places as​ needed.)

c. If the height requirements are changed to exclude only the tallest​ 5% of men and the shortest​ 5% of​ women, what are the new height​ requirements?

The new height requirements are at least__in. and at most__in.

(Round to one decimal place as needed.)

Answer 1

A) "Convert ft to inches."

The following information has been provided:

μ=62.6, σ=2.6

98.44% women meet the height requirement.

B)

99.69% men meet the height requirement.

C)

For men the P(X<72.041104792769) = 0.95

For women P(X<58.3233805699262) = 0.05

Hence the required heights are 58.3 and 72.04 inches.

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