Question

13. (3.37) 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 22.7 miles per gallon (mpg) and standard deviation 5.3 mpg. The quartiles of any distribution are the values with cumulative proportions 0.25 and 0.75. They span the middle half of the distribution What are the quartiles (+0.01) of the distribution of gas mileage? The first quartile is mpg The third quartile is mpg

Answer 1

Answer

We know that the formula for first quartile and third quartile is given as

Q1 = mean - 0.67*(standard deviation)

and Q3 = mean + 0.67*(standard deviation)

We have mean = 22.7 and standard deviation = 5.3

setting the values, we get

Q1 = mean - 0.67*(standard deviation) = 22.7 -(0.67*5.3) = 22.7-3.551 =19.15 mpg

And

Q3 = mean + 0.67*(standard deviation) = 22.7 +(0.67*5.3) = 22.7+3.551 =26.25 mpg

So, required values of first quartile and third quartile are 19.15 mpg an 26.25 mpg respectively.