Using the Central Limit Theorem · Try It 4
According to Boeing data, the 757 airliner carries 200 passengers and has doors with a height of 72 inches. Assume for a certain population of men we have a mean height of 69.0 inches and a standard deviation of 2.8 inches.
(a) What doorway height would allow 95% of men to enter the aircraft without bending?
(b) Assume that half of the 200 passengers are men. What mean doorway height satisfies the condition that there is a 0.95 probability that this height is greater than the mean height of 100 men?
(c) For engineers designing the 757, which result is more relevant: the height from part a or part b? Why?
Its source prints no answer for this problem, so there's nothing to check against.
OpenStax, Introductory Statistics 2e · §7.3 Using the Central Limit Theorem · Try It 4
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