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# Redesign of Ejection Seats When women were allowed to ISBN: 9780321836960 18

## Solution for problem 19BSC Chapter 6.5

Elementary Statistics | 12th Edition

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Problem 19BSC

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?  Step-by-Step Solution:

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.

Step 3 of 3

##### ISBN: 9780321836960

This textbook survival guide was created for the textbook: Elementary Statistics, edition: 12. This full solution covers the following key subjects: Women, ejection, seats, Probability, designed. This expansive textbook survival guide covers 121 chapters, and 3629 solutions. Elementary Statistics was written by and is associated to the ISBN: 9780321836960. The full step-by-step solution to problem: 19BSC from chapter: 6.5 was answered by , our top Statistics solution expert on 03/15/17, 10:30PM. Since the solution to 19BSC from 6.5 chapter was answered, more than 913 students have viewed the full step-by-step answer. The answer to “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?” is broken down into a number of easy to follow steps, and 138 words.

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