Final answer:
Approximately 70.79% of women have weights between 132 lb and 217 lb when considering a normal distribution with a mean of 170 lb and a standard deviation of 40 lb. Consequently, this indicates that a significant portion of women would be excluded from the usage of ejection seats designed with the specified weight range.
Step-by-step explanation:
The student asks about the percentage of women whose weights fall between the specified limits of military aircraft ejection seats designed for weights between 132 lb and 217 lb, given that women's weights are normally distributed with a mean of 170 lb and a standard deviation of 40 lb. To solve this, we use the properties of the normal distribution. First, we convert the weight limits into z-scores using the formula:
Z = (X - μ) / σ
• For 132 lb: Z = (132 - 170) / 40 = -0.95
• For 217 lb: Z = (217 - 170) / 40 = 1.175
Next, we look up these z-scores in a standard normal distribution table (or use a statistical calculator) to find the area under the curve, which represents the percentage of women within these weights. Let's assume these z-scores correspond to certain probabilities (e.g., 0.1711 for z=-0.95 and 0.8790 for z=1.175). The percentage of women with weights between the limits is the difference between these probabilities.
Percentage = (Probability at Z=1.175) - (Probability at Z=-0.95) Percentage = 0.8790 - 0.1711 Percentage = 0.7079 Percentage = 70.79%. Therefore, approximately 70.79% of women weigh between 132 lb and 217 lb according to this normal distribution, meaning a substantial number of women would be excluded from using the ejection seats with those specifications.