Section 71 36 You Explain It Miles per Gallon Elena conducts

Section 7.1

36. You Explain It! Miles per Gallon: Elena conducts an experiment in which she ?lls up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each ?ll-up. A histogram of the miles per gallon indicates that a normal distribution with a mean of 24.6 miles per gallon and a standard deviation of 3.2 miles per gallon could be used to model the gas mileage for her car.

(a) The ?gure represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve to the right of x = 26 is 0.3309. Provide two interpretations of this area.

Answer:

(b) The ?gure at the top of the next column represents the normal curve with m = 24.6 miles per gallon and s = 3.2 miles per gallon. The area under the curve between x = 18 and x = 21 is 0.1107. Provide two interpretations of this area.

Solution

a)

1. 33.09% of fill-ups have a miles-per-gallon greater than 26 mi/gal.

2. 100% - 33.09% = 66.91% of fill-ups have a miles-per-gallon less than 26 mi/gal.

******************

b)

1. 11.07% of fill-ups have a miles-per-gallon between 18 to 21 mi/gal.

2. 100% - 11.07 = 88.93% of fill ups are either less than 18 mi/gal or greater than 21 mi/gal. [