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 $169 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? $enter the dollar amount that would be more than 85% of operating costs

Answer 1

Solution:-

Given that,

mean = = $ 2087

standard deviation = = $ 169

a) Using standard normal table,

P(Z < z) = 20%

= P(Z < z ) = 0.20

= P(Z < -0.84 ) = 0.20  

z = -0.84

Using z-score formula,

x = z * +

x = -0.84 * 169 + 2087

x = $ 1945.04

$ 1945.04the dollar amount at which only 20% of the operating costs would be less.

b) Using standard normal table,

P(Z > z) = 65%

= 1 - P(Z < z) = 0.65  

= P(Z < z) = 1 - 0.65

= P(Z < z ) = 0.35

= P(Z < -0.39 ) = 0.35  

z = -0.39

Using z-score formula,

x = z * +

x = -0.39 * 169 + 2087

x = $ 2021.09

$ 2021.09 the dollar amount at which 65% of the operating costs would be more.

c) Using standard normal table,

P(Z > z) = 85%

= 1 - P(Z < z) = 0.85  

= P(Z < z) = 1 - 0.85

= P(Z < z ) = 0.15

= P(Z < -1.04) = 0.15  

z = -1.04

Using z-score formula,

x = z * +

x = -1.04 * 169 + 2087

x = $ 1911.24

$ 1911.24 the dollar amount that would be more than 85% of operating costs.