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 69 inches and a standard deviation of 2.8 inches.

Question

b) assume that half of the 200 passengers are men, what doorway height satisfies the condition that there is a .95 probability that this height is greater than the mean height of 100 men?

Answer 1

a)
The value of z such that P(Z<z)= 0.95 is z = 1.6449
Solving for x:
z =1.6449=(x-69.0)/2.8
x = 1.6449*2.8+69 = 73.6

b)
Solving for xbar:
z =1.6449=(xbar-69.0)/(2.8/sqrt(100))
xbar = 1.6449*0.28+69 = 69.5

Answer 2

0.8577