Question

The doorway of a specific style house is 71 inches. Men’s heights are normally distributed with a μ of 68.4 inches and σ of 1.9 inches. Women’s heights are normally distributed with a μ of 64.8 inches and a σ of 2.6 inches.

For the following use the same data for heights from above (no pun intended). To get into the police academy there are height requirements. A person needs to be at least five feet tall and no taller than 6.5 feet tall.

i. Determine the percentage of men that are too tall.

ii. Determine the percentage of men that are too short.

iii. Determine the percentage of women that are too tall.

iv. Determine the percentage of women that are too short.

v. Determine the probability that the μ of a sample of 100 men will be above greater than 70 inches.

vi. Determine the probability that the μ of a sample of women will be below 67 inches.

vii. Determine the 25th and 75th percentile for men.

viii. Determine the values of the heights of the middle 99% of women.

Answer 1

(there are more than 4 parts, as per policy i am answering first 4 parts)

6.5 feet = 75 inches

5 feet = 60 inches

x = height in inches

i.

percentage of men that are too tall = P(x>=75 inches) * 100%

percentage of men that are too tall = 0.0003 * 100% = 0.03%

ii.

percentage of men that are too short = P(x<=60 inches) * 100%

percentage of men that are too short = 0 * 100% = 0%

iii.

percentage of women that are too tall = P(x>=72 inches) * 100%

percentage of women that are too tall = 0 * 100% = 0%

iv.

percentage of women that are too short = P(x<=60 inches) * 100%

percentage of women that are too short = 0.0324 * 100% = 3.24%

(please UPVOTE)

P(z<Z) table :