Question

Assume that the mean hourly cost to operate a commercial airplane follows the normal distribution with a mean of $1660 per hour and a standard deviation of $190.

What is the maximum operating cost for the lowest 2% of the airplanes? (Round z-score computation to 2 decimal places and the final answer to 1 decimal place.)

Maximum operating cost           $

Answer 1

Mean of the operating cost of a commercial airplane $1660  per hour and the standard deviation is a $190 .

Let X be the random variable.

Now

And

2 percent of the observations lie below X1.

P(z < z1 ) = 0.02

i.e

0.5 - P(-z1 < z < 0) = 0.02

P(-z1 < z < 0) = 0.5-0.02

P(-z1 < z < 0) = 0.48

There fore. -z1 = 2.05 ( normal table value )

i.e z1 = -2.05

Hence

x1= 1270.5

Maximum Operating cost for the lowest 2 percent of the airlines is $1270.5

Normal distribution table :