Question

When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been designed for men only. The ACES-II ejection seats were designed for men weighing between 140 pounds and 211 pounds. The population of women has normally distributed weights with a mean of 143 pounds and a standard deviation of 29 pounds (based on data from the National Health Survey).

a. If 1 woman is randomly selected, find the probability that her weight is between 140 pounds and 211 pounds.

Answer 1

To find the probability that a randomly selected woman's weight is between 140 and 211 pounds, calculate the z-scores and use a standard normal distribution table or calculator.

Step-by-step explanation:

To find the probability that a randomly selected woman's weight is between 140 and 211 pounds, we need to calculate the z-scores for these weights using the formula:

z = (x - μ) / σ

where x is the weight, μ is the mean weight, and σ is the standard deviation. Once we have the z-scores, we can find the corresponding probabilities using a standard normal distribution table or a calculator.

For the weight of 140 pounds:

z = (140 - 143) / 29 ≈ -0.10

For the weight of 211 pounds:

z = (211 - 143) / 29 ≈ 2.34

Using the standard normal distribution table or a calculator, the probability that a woman's weight is between 140 and 211 pounds is approximately 0.4920, or 49.20%.