L 1 21 of 21 (10 complete) An airliner carrmies 300 passengers and has doors wit
ID: 3318177 • Letter: L
Question
L 1 21 of 21 (10 complete) An airliner carrmies 300 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69 0 in and a standard deviation of 2 8 in. Complete parts (a) through (d) a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending The probability is (Round to four decimal places as needed) b. If half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 72 in. The probability is (Round to four decimal places as needed) c. When considening the comfort and safety of passengers, which result is more 0 A. The probability from part (b) is more re relevant the probabilty from part (a) or the probablity from part (b)? Why? n of flights where the mean height of the male passengers will be less than the door height from part (b) is more relevant because ia shows the proportion of male passengers that will not need to bend The probability from part (a) is more relevant because D. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend it shows the proportion of flights where the mean height of the male passengers will be less than the door height of flights where the O C. d. When considering the comfort and safety of passengers, why are women ignored in this case? Therefore, it is more m important that men not have to bend than it is importanst that women not have to bend Since men are generally taller than women, it is more difficult for them to bend when entering the area B. Since men are generally taller than women, a design that accommodates a suitable proportion of men will ecessanily accommodate a greater proportion of women o A. O C. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of womenExplanation / Answer
a) Formula: Z = (X-mean)/sd
P(X < 72) = P(Z < (72-69)/2.8) = P(Z < 1.07) = 0.8577
b) Formula: Z = (X_bar - mean)/(SD/sqrt(N))
P(X < 72) = P(Z < (72-69)/(2.8/sqrt(150)) = P(Z < 13.12) = 1
c) The probability from part(b) is more relevant because it shows the proportion of male passengers that will not need to bend
d) Option B. Since men are generally taller than women, a design that accomodates a suitable proportion of men will necessarily accomodate a greater proportion of women
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