Question

(3.38) NOTE: The numerical values in this problem have been modified for testing purposes.

In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles. There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.9 miles per gallon (mpg) and standard deviation 5.2 mpg.

The quintiles of any distribution are the values with cumulative proportions 0.20, 0.40, 0.60, and 0.80. What are the quintiles of the distribution of gas mileage?

(Use software)

The first quintile is (±±0.01 mpg)  mpg.______

The second quintile is (±±0.01 mpg)  mpg._____

The third quintile is (±±0.01 mpg)  mpg.____

The fourth quintile is (±±0.01 mpg)  mpg._____

Answer 1

Suppose X follows approximately Normal with mean 22.9 miles per gallon (mpg) and standard deviation 5.2 mpg.

Here we need to find X scores for probabilities 0.20, 0.40, 0.60 and 0.80

Let's use excel:

For probability = 0.20

x = "=NORMINV(0.20, 22.9, 5.2)" = 18.52 mpg

The first quintile is (±±0.01 mpg)  mpg. 18.52

For probability = 0.40

x = "=NORMINV(0.40, 22.9, 5.2)" = 21.58 mpg

The second quintile is (±±0.01 mpg)  mpg. 21.58

For probability = 0.60

x = "=NORMINV(0.60, 22.9, 5.2)" = 24.22mpg

The third quintile is (±±0.01 mpg)  mpg. 24.22

For probability = 0.80

x = "=NORMINV(0.80, 22.9, 5.2)" = 27.28 mpg

The fourth quintile is (±±0.01 mpg)  mpg. 27.28