Time Limit: 01:00:00 his Question: 10 pts Submit Qui 5 of 10 (0 complete)v This

Question

Time Limit: 01:00:00 his Question: 10 pts Submit Qui 5 of 10 (0 complete)v This Quiz: 100 pts possib An airliner carries 300 passengers in. Complete parts (a) through (d) 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 28 a. If a male passenger is randomly selected, find the probability that he can fit through the doorway wthout belnding 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 78 in The probability is (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers which result is more relevant the probablit fom part (aj or the probablity fom part (oj? why? O B. The probability from part (b) is more relevant because it shows the proportion of fights where the mean height of the maie passengers nill be les than the O C. /The probability from part (a) is more relevant because in O D. The probability from part (b) is more relevant shows the Cick to select your answers) O A. The probability from part (a) is more relevant because it shows the proportion of male passengers that well not need to bend e esshan b shons the praponion of tignts whe the mean height of hemaeas ause it shows the proporton of male passengers that well not need to bencd door height door height

Explanation / Answer

Here' the answer with detailed solution and formulae:

a. There are 300 people with a door of height of 78 inches
Mean = 69 inches
Stdev= 2.8 inches

We will use the above normal dist. params to solve / standardize distributions.

a. P(male passenger is randomly selected) = P(X>78) = P(Z> (78-69)/2.8) = P(Z>3.21) = .0007

b. P(X<78) = P(Z< 78-78 / (2.8/sqrt(150)) = P(Z<0) =.5000

c. A is correct. For safety and comfort we shouldn't allow men to bend thier neck/head as
it will be serious concern. Thus, we should take care that their height is less door'. Thus, a is more relevant

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