Question

A survey found that​ women's heights are normally distributed with mean 62.2 in. and standard deviation 2.2 in. The survey also found that​ men's heights are normally distributed with mean 67.3 in. and standard deviation 3.3 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts​ (a) and​ (b) below.

a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​park?

The percentage of men who meet the height requirement is ___

(Round to two decimal places if needed)

b. If the height requirement 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 ___ in. and a maximum of ___ in.

(Round to two decimal places if needed)

Answer 1

Given data :

Men height mean

=62.2 in

Men stadndard deviation

a)

height requirements of a minimum of 57 in. and a maximum of 63 in

Z value of 57

from Normal distribution Table

P(-2.36) = 0.0091

Z value of 63

from Normal distribution Table

P(0.36) = 0.6406

The Probability of men who meet the height requirement = P(0.36)-P(-2.36)

The Probability of men who meet the height requirement =0.6406-0.0091

The Probability of men who meet the height requirement =0.6315

The percentage of men who meet the height requirement is 63.15%

b)

If the height requirement are changed to exclude only the tallest 50% of men and the shortest 5% of men,

P(Z-min)=0.05

P(Z-max)=0.5

From normal distribution table.

P(Z-min)=0.05

Z-min = -2.575

Xmin =56.535in

From normal distribution table.

P(Z-max)=0.5

Z-max = 0

Xmin =62.2in

The new height requirements are a minimum of 56.53 in. and a maximum of 62.2in.