Question

Assume that military aircraft use ejection seats designed for men weighing between 135.6 and 201 lb. If women's weights are normally distributed with a mean of 174.9 lb and a standard deviation of 41.1 lb , what percentage of women have weights that are within those limits ? any women excluded with those specifications ?

The percentage of women that have wieghts between those limits is: ____%

Answer 1

Approximately 56.83% of women have weights that fall within the military aircraft ejection seat limits of 135.6 to 201 lb. This is calculated using z-scores and the standard normal distribution.

Step-by-step explanation:

To find the percentage of women who fall within the ejection seat weight limits for military aircraft, we need to calculate the probabilities corresponding to the weights between 135.6 and 201 lb, given that the women's weights are normally distributed with a mean (μ) of 174.9 lb and a standard deviation (σ) of 41.1 lb.

First, we will convert the weight limits into z-scores using the formula:

z = (
x - μ) /
σ

For the lower limit (135.6 lb):
zlower = (135.6 - 174.9) / 41.1 = -0.956

For the upper limit (201 lb):
zupper = (201 - 174.9) / 41.1 = 0.635

Next, we need to look these z-scores up in the standard normal distribution table to find their corresponding probabilities. The probability for zlower is approximately 0.1696, and for
zupper is approximately 0.7379.

The difference between these probabilities gives us the proportion of women who fall within the weight limits:

Percentage within limits = (0.7379 - 0.1696) × 100 = 56.83%

Therefore, approximately 56.83% of women have weights that fall within the specified limits for the ejection seats. Yes, there will be women who are either too light or too heavy for the ejection seats and are thus excluded based on these specifications.