Question

The Air Transport Association of America reports that the average operating cost of an MD-80 jet airliner is $2,270 per hour, with a standard deviation of $173 per hour. Operating costs are normally distributed.

(a) At what operating cost would only 20% of the operating costs be less than this value?

(b) At what operating cost would 65% of the operating costs be more than this value?

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

Answer 1

Using the z-scores from the standard normal distribution, the operating costs are determined to be $2,124.68 for the lower 20%, $2,202.53 for the upper 35%, and $2,449.92 for costs higher than 85% of all costs.

Step-by-step explanation:

The question asks to determine certain operating costs for an MD-80 jet airliner, where costs are normally distributed. We will use the average operating cost and the standard deviation provided to find the specific costs that correspond to given percentages of the distribution.

(a) Operating Cost for Lower 20%

To determine the operating cost that is higher than only 20% of the costs we need to find the z-score for 0.20 in the standard normal distribution table and then use the formula cost = mean + (z-score × standard deviation). The z-score associated with 20% is around -0.84. Using this we get:

Cost = $2,270 + (-0.84 × $173) = $2,270 - $145.32 = $2,124.68.

(b) Operating Cost for Upper 35%

Since 65% of the costs are higher, we're looking at the 35th percentile. The z-score for 0.35 is approximately -0.39. Applying our formula:

Cost = $2,270 + (-0.39 × $173) = $2,270 - $67.47 = $2,202.53.

(c) Operating Cost Above 85%

For this calculation, we need the z-score for the 85th percentile, which is roughly 1.04. Using the formula:

Cost = $2,270 + (1.04 × $173) = $2,270 + $179.92 = $2,449.92.