Redesign of Ejection Seats When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. Weights of women are now normally distributed with a mean of 165.0 lb and a standard deviation of 45.6 lb (based on Data Set 1).

a. If 1 woman is randomly selected, find the probability that her weight is between 140 lb and 211 lb.

b. If 36 different women are randomly selected, find the probability that their mean weight is between 140 lb and 211 lb.

c. When redesigning the fighter jet ejection seats to better accommodate women, which probability is more relevant: the result from part (a) or the result from part (b)? Why?

Answer :

Step 1 of 3 :

Given, When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were designed for men weighing between 140 lb and 211 lb. Weights of women are now normally distributed with a mean of 165.0 lb and a standard deviation of 45.6 lb

If 1 woman is randomly selected,The claim is to find the probability that her weight is between 140 lb and 211 lb

Z =

Where , = 140

Z =

= -0.55

Then, P(z > -0.55)

= P(z < 0.55)

= 0.2912 (from area under normal curve table)

Where , = 211

Z =

= 1.01

Then, P(z < 1.01)

= 0.8438 (from area under normal curve table)

P(-0.55 < z < 1.01) = P(z < 1.01) - P( z < -0.55)

= 0.8438 - 0.2912

which have a probability of 0.5526 between them.

Step 2 of 3 :

b) The claim is to find the probability that her weight is between 140 lb and 211 lb

Where, n = 36

Z =

Where , = 140

Z =

= -3.29

Then, P(z < -3.29)

= 0.0005 (from area under normal curve table)

Z =

When, = 211

Z =

= 6.05

Then, P(z < 6.05)

= 0.9999 (from area under normal curve table)

P(-3.29 < z < 6.05) = P(z < 6.05) - P( z < -0.55)

= 0.9999 - 0.0005

which have a probability of 0.9994 between them.