Question

1. The average weight of an airline passenger’s suitcases is 45 pounds with a standard deviation of 2 pounds. If 16% of the suitcases are overweight, find the maximum weight allowed by the airline. Assume the variable is bell – shaped distributed. Hint: Sketch and label a normal model to help answer the question.

Answer 1

Solution :

Given that,  

mean = = 45

standard deviation = = 2

Using standard normal table ,

P(Z > z) = 16%

1 - P(Z < z) = 0.16

P(Z < z) = 1 - 0.16

P(Z < 0.99) = 0.84

z = 0.99

Using z-score formula,

x = z * +

x = 0.99 * 2 + 45 = 46.98

maximum weight = 46.98