An airliner carries 150 passengers and has doors with a height of 78 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(B) If half of the 150 passengers are men, find the probabilty that the mean height of the 75 men is less that 72 in. The probability is _____ Round to four decimal places(C) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?(D) The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
A) Prob that a random man from 150 can fit without bending
= P(X<78) = P(Z<3.214)=1.0000
B) n =75
Sample std dev =
P(X bar <72) = P(Z<9.28) = 1.00
C) Prob of B is more relevent because average male passengers would be more relevant than a single person
(D) The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
D. If 11.60 of them 5, then in your proportions they would need to be on the same side (both numerators or both denominators) and D is the only answer where this is true.
