Question

when women were finally allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. the ejection seats were designed for men weighing between 130 lb and 201 lb. weights of women are now normally distributed with a mean of 169 lb and a standard deviation of 35 lb. complete parts (a) through (c) below.
a. if 1 woman is randomly selected, find the probability that her weight is between 130 lb and 201 lb.
the probability is approximately □ (round to four decimal places as needed.)

Explanation:

Step1: Calculate z - scores

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $\mu = 169$ (mean), $\sigma = 35$ (standard deviation).
For $x = 130$, $z_1=\frac{130 - 169}{35}=\frac{- 39}{35}\approx - 1.11$.
For $x = 201$, $z_2=\frac{201 - 169}{35}=\frac{32}{35}\approx0.91$.

Step2: Find probabilities using z - table

We want $P(130$P(-1.11From the standard normal table, $P(Z < 0.91)=0.8186$ and $P(Z < - 1.11)=0.1335$.
So $P(-1.11

Answer:

$0.6851$