Ask Question
3 August, 20:18

Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U. S. Marine Corps requires that men have heights between 64 and 78 inches. Find the percent of men meeting these height requirements.

+1
Answers (1)
  1. 3 August, 20:35
    0
    Answer: 96.2%

    Step-by-step explanation:

    Assume that the heights of American men are normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = heights of American men.

    µ = mean height

    σ = standard deviation

    From the information given,

    µ = 69.0 inches

    σ = 2.8 inches

    the probability of men that have heights between 64 and 78 inches is expressed as

    P (64 ≤ x ≤ 78)

    For x = 64,

    z = (64 - 69) / 2.8 = - 1.79

    Looking at the normal distribution table, the probability corresponding to the z score is 0.037

    For x = 78,

    z = (78 - 69) / 2.8 = 3.2

    Looking at the normal distribution table, the probability corresponding to the z score is 0.999

    Therefore,

    P (64 ≤ x ≤ 78) = 0.999 - 0.037 = 0.962

    Therefore, the percent of men meeting these height requirements is

    0.962 * 100 = 96.2%
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Assume that the heights of American men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U. ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers