ne box providcd. Central Limit Theorem - Redesign of Ejection Seats: In an carli
ID: 3048943 • Letter: N
Question
ne box providcd. Central Limit Theorem - Redesign of Ejection Seats: In an carlier ca Scott (hen Captain Scott) was Chief of Staff at the Navy's Education Command in reer, Dr FL, where the Navy provides initial flight training to Naval Aviators, both Navy and Marine Corps. This issue actually came up: the redesign of fighter aircraft ejection seats to accommodate women pilots. The seats had for men only. The ACES-II 140 lb and 211 lb. Weights of women are accurately modeled with the random variable X~N (165.0,45.6) in pounds (lb) been originally designed ejection seats were designed for men weighing between a. If one woman is randomly selected, find the probability that her weight is between 140 lb and 211 lb. b. Suppose a random sample of 36 women is taken. Find the probability that their mean weight is between 140 lb and 211 lb. When redesigning the fighter jet ejection seats to better accommodate women which probability is more relevant: the results from part (a) or the result from c.Explanation / Answer
a) P(140 < X < 211) = P((140 - mean)/sd < (X - mean)/sd < (211 - mean)/sd)
= P((140 - 165)/45.6 < Z < (211 - 165)/45.6)
= P(-0.55 < Z < 1)
= P(Z < 1) - P(Z < -0.55)
= 0.8413 - 0.2912
= 0.5501
c) The probability from part(b) is more relevant.
b) P(140 < X < 211) = P((140 - mean)/(sd/sqrt(n)) < (X - mean)/(sd/sqrt(n)) < (211 - mean)/(sd/sqrt(n)))
= P((140 - 165)/(45.6/sqrt(36)) < Z < (211 - 165)/(45.6/sqrt(36)))
= P(-3.29 < Z < 6.05)
= P(Z < 6.05) - P(Z < -3.29)
= 1 - 0.0005
= 0.9995
c)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.