Final answer:
Using the normal distribution of women's weights with a mean of 173.2 lb and a standard deviation of 44.4 lb, we calculate z-scores for the weight limits and find the percentage corresponding to these scores through a standard normal distribution table or calculator, representing the percentage of women within the ejection seat's weight limits.
Step-by-step explanation:
To calculate the percentage of women who are within the weight limits for a military aircraft ejection seat designed for men weighing between 136.3 lb and 215 lb, we use the normal distribution of women's weights. We know that women's weights are normally distributed with a mean (μ) of 173.2 lb and a standard deviation (σ) of 44.4 lb.
First, we find the z-scores for the lower and upper weight limits using the formula z = (X - μ) / σ, where X is the weight limit. For the lower limit, 136.3 lb, the z-score is:
z(lower) = (136.3 - 173.2) / 44.4 ≈ -0.83
For the upper limit, 215 lb, the z-score is:
z(upper) = (215 - 173.2) / 44.4 ≈ 0.94
We then use a standard normal distribution table or a calculator with statistics functions to find the percentage of women within these z-score limits. The areas under the standard normal curve corresponding to z(lower) and z(upper) give us the percentage of women who have weights between 136.3 lb and 215 lb.
The percentage of women within these limits will be roughly the area under the normal curve between z(lower) and z(upper).