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Assume that military aircraft use ejection seats designed for men weighing between 146 lb and 212 lb. If​ women's weights are normally distributed with a mean of 173.3 lb and a standard deviation of 41.7 ​lb, what percentage of women have weights that are within those​ limits? Are many women excluded with those​ specifications?

Respuesta :

Answer:

56.69% of women belong within the given limits of seats. Yes, a majority of 43.31% of women are excluded with those​ specifications.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 173.3 lb

Standard Deviation, σ = 41.7 ​lb

We are given that the distribution of women's weight is a bell shaped distribution that is a normal distribution.

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

P(weighing between 146 lb and 212 lb)

[tex]P(146 \leq x \leq 212)\\\\ = P(\displaystyle\frac{146 - 173.3}{41.7} \leq z \leq \displaystyle\frac{212-173.3}{41.7})\\\\ = P(-0.6546 \leq z \leq 0.9280)\\\\= P(z \leq 0.9280) - P(z < -0.6546)\\= 0.8233 -0.2564 = 0.5669 = 56.69\%[/tex]

Thus, 56.69% of women belong within the given limits of seats. Yes, a majority of 43.31% of women are excluded with those​ specifications.

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