Question

4) The time it takes to fly from Detroit to Honolulu is normal distributed. It is determined that 10% of all flights take more than 10.256 hours while 5% take less than 9671 hours. If a flight is selected at random, what is the probability that it will take less than 10.100 hours?

Answer 1

z-value for 90% = 1.28
using central limit theorem,
x = mean + z * sigma
10.256 = mean + 1.28*sigma ... 1

z-value for 5% = -1.65
using central limit theorem,
x = mean + z * sigma
9.671 = mean -1.65 *sigma ... 2

Solving equation 1 and 2, we get
sigma = 0.1997

mean = 10.0004

P(X < 10.100)
= P(z < (10.100 - 10.0004)/0.1997)
= P(z < 0.4987)
= 0.6910