Question

Assume that military aircraft use ejection seats designed for men weighing between 135.3 lb and 220 ib. If women's weights are normally distributed with a mean of 160.3 lb and a standard deviation of 46.2 lb, what percentage of women have weights that are within those limits? (b)Are many women excluded with those specifications?The percentage of women that have weights between those limits is %

Answer 1

Answer:

60.8%

Explanation:

• The mean of the women's weight = 160.3 lb

,

• The standard deviation = 46.2 lb

To find the percentage of women within those limits, first, find the z-scores for x-values: 135.3 lb and 220 lb.

$\begin{gathered} Z-\text{Score}=\frac{X-\text{Mean}}{S\mathrm{}D} \\ At\text{ X=}135.3,Z-\text{Score}=\frac{135.3-\text{1}60.3}{46.2}=-0.5411 \\ At\text{ X=}220,Z-\text{Score}=\frac{220-\text{1}60.3}{46.2}=1.2922 \end{gathered}$

Next, using the z-score table, we find the required probability:

[tex]P(-0.5411• Therefore, the percentage of women that have weights between those limits is 60.8%.,

• (b) No. A smaller percentage (39.2%) of women are excluded with those specifications.