You Explain it Elana conducts an experiment in which she fil

You Explain it! Elana conducts an experiment in which she fills up the gas tank on her Toyota Camry 40 times and records the miles per gallon for each fill-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 miler per gallon could be used to model the gas mileage for her car.

a) The figure 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.

b) THe figure 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 is between x=18 and x=21 is 0.1107. Provide two interpretations of this area.

Solution

a)

Area to right of x=26 is 0.3309, the 2 interpretations are as follows:

1) Probability that the miles per gallon of the Toyota Camry is greater than 26 is 0.3309

2) Probability that the miles per gallon of the Toyota Camry is less than 26 is 1 - above = 0.6691

b) Area between x=18 and x = 21 is 0.1107; the 2 interpretations are as follows:

1) Probability of getting mileage between 18 to 21 is 0.1107

2) probability of getting mileage less than 18 and more than 21 is 1 - 0.1107 = 0.8893