In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg. The 2008 Chevrolet Malibu with a four-cylinder engine has combined gas mileage 25 mpg.
a. What percent of all vehicles have worse gas mileage than the Malibu?
b. How high must a 2008 vehicle’s gas mileage be in order to fall in the top 5% of all vehicles? (The distribution omits a few high outliers, mainly hybrid gas-electric vehicles.)
c. 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 of the distribution of gas mileage?
Gas mileage of the first quartile:
Gas mileage of the third quartile:
d. 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?
Gas mileage of 0.20 of the distribution:
Gas mileage of 0.40 of the distribution:
Gas mileage of 0.60 of the distribution:
Gas mileage of 0.80 of the distribution: