5 Given the parameters that the Mens heights are normally di

5. Given the parameters that the Men’s heights are normally distributed with mean 69.5 inches and standard deviation 2.4 inches. Women’s heights are normally distributed with mean 63.8 inches and standard deviation 2.6 inches. Most of the live characters at Disney World have height requirements with a minimum of 4 ft 8 in. and a maximum of 6 ft 3 in. a. Find the percentage of women meeting the height requirement. b. Find the percentage of men meeting the height requirement. c. If the height requirments are changed to exclude only the tallest 5% of men and the shortest 5% of women, what are the new height requirement?

Solution

Males height Normal (69.5, 2.4)

Women height Normal (63.8, 2.6)

Range for height is (4\'8\", 6\'3\")

a) To find percent of women

56<x<75 convert to z score for women

-7.8/2.4 <z<11.2/2.4

P(-3.25<z<4.67) = 1.0000

Nearly 100% women meet this requirement.

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b) P(-13.5/2.4<z<10.5/2.4)

= P(-5.63<z<4.38)

= 1.000

100% males meet this requirement.

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c) Exclude 5% of women means

z =-1.645

x = women height = 63.8-1.645(2.6)

=59.523 inches

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For males top 5%

z = 1.645

x= 69.5+2.4(1.645)

= 73.448

Hence new height requirements are

59.523 inches to 73.448 inches