In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection
ID: 3072150 • Letter: I
Question
In its Fuel Economy Guide for 2016 model vehicles, the Environmental Protection Agency provides data on 1170 vehicles. There are a number of high outliers, mainly hybrid gaselectric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1146 vehicles is approximately Normal with mean 23.0 miles per gallon (mpg) and standard deviation 4.9 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 is the first quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.
What is the third quartile of the distribution of gas mileage? Use Table A and give your answer rounded to two decimal places.
Explanation / Answer
mean = 23 , sd = 4.9
Z = (X - mean)/sd
for 1st quartile
P(Z < z) = 0.25
from table ,z =
X = mean + z* sd
= 23 - 0.67449 * 4.9
= 19.694999
for 3rd quartile
P(Z < z) = 0.75
from table ,z = 0.67449
X = 23 + 0.67449 * 4.9
= 26.305001
Please rate
-0.67449