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 5.1 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 first quintile is (±±0.01 mpg)  mpg.

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

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

Answer 1

mean μ=	22.9
standard deviation σ=	5.1000

for 20th percentile critical value of z=		-0.8416
therefore corresponding value=mean+z*std deviation=			18.61

hence first quintile is 18.62 mpg

for 40th percentile critical value of z=		-0.2534
therefore corresponding value=mean+z*std deviation=			21.61

second quintile is 21.61 mpg

for 60th percentile critical value of z=		0.2534
therefore corresponding value=mean+z*std deviation=			24.19

third quintile is 24.19 mpg

for 80th percentile critical value of z=		0.8416
therefore corresponding value=mean+z*std deviation=			27.19

4th quintile is 27.19 mpg