A survey found that women\'s heights are normally distributed with mean 63.2 in.

Question

A survey found that women's heights are normally distributed with mean 63.2 in. and standard deviation 2.6 in. The survey also found that men's heights are normally distributed with a mean 67.2 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. f 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.)

Explanation / Answer

a) We know 1 feet = 12 inch

P(57<W<75)

= P((57-63.2)/2.6<Z<((75-63.2)/2.6)

= 99.14%

So, answer is 99.14%

b) P(57<M<75)

= P((57-67.2)/2.7<Z<((75-67.2)/2.7)

= 99.80%

So, answer is 99.80%

c) Tallest 5% of men

= 1.645*2.7+67.2 = 71.6 inch

Shortest 5% of women

= -1.645*2.6+63.2 = 58.9 inch

So, new height requirements are at least 58.9 in and at most 71.6 inch

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