Question

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.

Answer 1

Answer:

Step-by-step explanation:

x, height of men is N(69, 2.8)

Sample size n =150

Hence sample std dev = $\frac{2.8}{\sqrt{150} } =0.229$

Hence Z score = $\frac{x-69}{0.229}$

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 = $\frac{2.8}{\sqrt{75} } =0.3233$

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.