Question

A survey found that womens heights are normally distributed with mean 62.7 in and standard deviation 3.5 in. the survey also found that mens heights are normally distributed with a mean 67.1 and SD 3.8 inch. Most of the live characters employed at an amusement park have height requirements of a minimum of 56in and a maximum of 64in.

A) most of the live characters at an amusement park have height requirements with a minimum of 4ft 9in and a maximum of 6ft 4in find the percentage of women meeting the height requirement

the percentage of woment who meet the height requirement?

(round to two decimal places as needed)

b) find the percentage of men meeting the height requirement

the percentage of men meeting the height requirement

(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=62.7, σ=3.5

We need to compute Pr(57≤X≤76). The corresponding z-values needed to be computed are:

Therefore, we get:

94.82% women meet the height requirement.

B)

The following information has been provided:

μ=67.1, σ=3.8

We need to compute Pr(57≤X≤76). The corresponding z-values needed to be computed are:

Therefore, we get:

98.65% men meet the height requirement.

C)

For men the P(X<73.3504437824156) = 0.95

For women P(X<56.9430123056698) = 0.05

Hence the required heights are 56.9 and 73.4 inches.

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