Question

1. According to Boeing data, the 757 airliner carries 200 passengers and has doors with a mean height of 72 inches. Assume for a certain population of men we have a mean of 69.0 inches and a standard deviation of 2.8 inches.

a) What mean 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?

Answer 1

solution let x be the random wariable denoting the mean height. lx - 68 Tx = 2.8 The 25th Percentile = the height of the doorway that would allow 35th of men to enter the aircraft without bending The 3 value for g5th percentile is 3=196 x - 4x = 196 x = 196 8x + 4x - 1.96 x 28 +69 = 74.49 Given 4 x 4 = 69 for 95th percentile for we are looking sample of 100 men a random

3 – 196 X-4 - 196 x = 1960th - 196x2.8 169 Too = 69.55 when designing the doorway height, we need to incorporate as much variability as possible inorder to accomodate as many Passenger as possible. Therefore we need to use the result based on part
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