Question

In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency provides data on 11701170 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 11461146 vehicles is approximately Normal with mean 23.023.0 miles per gallon (mpg) and standard deviation 4.94.9 mpg.

The quartiles of any distribution are the values with cumulative proportions 0.250.25 and 0.75.0.75. They span the middle half of the distribution.

What is the first quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.

?1=Q1=

mpg

What is the third quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.

?3=

Answer 1

first quartile of the distribution of gas mileage

µ=   23                  
σ =    4.9                  
proportion=   0.25                  
                      
Z value at    0.25   =   -0.674   (excel formula =NORMSINV(   0.25   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -0.674   *   4.9   +   23  
X   =   19.695              
so, Q1 = 19.70

-----------------------------------------

µ=   23                  
σ =    4.9                  
proportion=   0.75                  
                      
Z value at    0.75   =   0.674   (excel formula =NORMSINV(   0.75   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   0.674   *   4.9   +   23  
X   =   26.30              
So, Q3 = 26.30