Question

The Boeing 757 – 200 ER airliner carries 200 passengers and has doors with a height of 72 inches. Heights of men are normally distributed with a mean of 68.6 inches and standard deviation of 2.8 inches.

a.If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. Round your final answer to four decimal places.

b.If half of the 200 passengers are men, find the probability that the mean height of 100 men is less than 72 inches. Round your final answer to four decimal places.

c.When considering the comfort and safety of passengers, which result is more relevant, the probability in part a or part b. Explain.

Answer 1

Solution :

Given that ,

mean = = 68.6

standard deviation = = 2.8

a) P(x < 72) = P[(x - ) / < (72 - 68.6) / 2.8]

= P(z < 1.21)

Using z table,

= 0.8869

b) n = 100

= = 68.6

= / n = 2.8 / 100 = 0.28

P( < 72) = P(( - ) / < (72 - 68.6) / 0.28)

= P(z < 12.14)

Using z table

= 1

c) The probability from part ( a) is more relevant because it shows the proportion of male passengers that will not need to bend