Question

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all males (Accommodating 100% of males would require very wide seats that would be much too expensive.) Men have hip breadths that are normally distributed with a mean of 14.5 inches and a standard deviation of 1.1 inches. Find the 99th percentile of hip breadths for men.

Answer 1

To find the 99th percentile of hip breadths for men, the Z-score can be calculated using the Z-score formula and looked up in a standard normal distribution table.

Step-by-step explanation:

To find the 99th percentile of hip breadths for men, we can use the Z-score formula. The Z-score is calculated as (X - mean) / standard deviation, where X is the value we want to find the percentile for. The Z-score can then be looked up in a standard normal distribution table to find the corresponding percentile. In this case, we want to find the Z-score such that the area to the left is 0.99. By looking up this Z-score, we can then solve for X using the Z-score formula.

Let's calculate the Z-score:

Z = (X - mean) / standard deviation

0.99 = (X - 14.5) / 1.1

Solving for X:

X = (0.99 * 1.1) + 14.5

X ≈ 16 inches

Therefore, the 99th percentile of hip breadths for men is approximately 16 inches.