Question

Fuel economy estimates for automobiles built one year predicted a mean of 26.8 mpg and a standard deviation of 5.2 mpg for highway driving. Assume that a Normal model can be applied. Use the 68-95-99.7 Rule to complete parts a) through e) a) Draw the model for auto fuel economy. ОА. OC A A A 14 21 b) In what interval would you expect the central 95% of autos to be found? Using the 88-95-99.7 rule, the central 95% of autos can be expected to be found in the interval from (Do not round. Type integers or decimals.) to mpg. c) About what percent of autos should get more than 32 mpg? Using the 88-95-99.7 rule, about % of autos should get more than 32 mpg. (Do not round. Type an integer or a decimal.) d) About what percent of autos should get between 32 and 37.2 mpg? Using the 68-95-99.7 rule, about % of autos should get between 32 and 37.2 mpg. (Do not round. Type an integer or a decimal.) e) Describe the gas mileage of the best 2.5% of cars. Choose the correct answer below. O A. They get more than 42.4 mpg. OB. They get more than 37.2 mpg OC. They get less than 21.6 mpg. OD. They get more than 32 mpg.

Answer 1

a) Option - C is correct graph.

b) According to empirical rule about 95% of the data fall within two standard deviation from the mean.

26.8 - 2 * 5.2 = 16.4

26.8 + 2 * 5.2 = 37.2

The central 95% of autos can be expected to be found in the interval from 16.4 to 37.2.

c) 26.8 + 5.2 = 32

32 is one standard deviation above the mean.

According to empirical rule about 68% of the data fall within one standard deviation from the mean.

So 34% of adults should get more than 32 mpg.

d) 26.8 + 5.2 = 32

   26.8 + 2 * 5.2 = 37.2

34% of the data fall within the mean 26.8 and 32.

47.5% of the data fall within the mean 26.8 and 37.2.

47.5% - 34% = 13.5%

13.5% of adults should get between 32 and 37.2 mpg.

e) 26.8 + 2 * 5.2 = 37.2

Option - B) They get more than 37.2 mpg.