Question

According to the Air Transport Association of America, the average operating cost of an MD-80 jet airliner is $2,087 per hour. Suppose the operating costs of an MD-80 jet airliner are normally distributed with a standard deviation of $163 per hour. (Round the value of z to 2 decimal places. Round your answers to 2 decimal places.)

(a) At what operating cost would only 20% of the operating costs be less? $ enter the dollar amount at which only 20% of the operating costs would be less

(b) At what operating cost would 65% of the operating costs be more? $ enter the dollar amount at which 65% of the operating costs would be more

(c) What operating cost would be more than 85% of operating costs?

Answer 1

Solution :

Given that,  

mean = = $2087

standard deviation = = $163

Using standard normal table ,

(a)

P(Z < z) = 20%

P(Z < -0.84) = 0.2

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 163 + 2087 = 1950.08

$1950.08

operating cost $1950.08

(b)

P(Z > z) = 65%

1 - P(Z < z) = 0.65

P(Z < z) = 1 - 0.65

P(Z < -0.39) = 0.35

z = -0.39

Using z-score formula,

x = z * +

x = -0.39 * 163 + 2087 = 2023.43

operating cost $2023.43

(c)

P(Z > z) = 85%

1 - P(Z < z) = 0.85

P(Z < z) = 1 - 0.85

P(Z < -1.04) = 0.15

z = -1.04

Using z-score formula,

x = z * +

x = -1.04 * 163 + 2087 = 1917.48

operating cost $1917.48