Fuel economy estimates for automobiles in one year predicted a mean of 27.2 mpg and a standard deviation of 5.8 mpg.

a) Draw the model for auto fuel economy.

b) In what interval would you expect the consumption to be, using the 68-95-99.7 rule?

c) About what percent of autos should get more than 33 mpg, using the 68-95-99.7 rule?

d) About what percent of autos should get between 33 and 38 mpg, using the 68-95-99.7 rule?

e) Describe the mileage of the best 25% of cars.

In this high school mathematics question, we use the mean and standard deviation to draw a model for auto fuel economy. We apply the 68-95-99.7 rule to estimate the range of fuel economy and calculate the percentage of autos with specific mileage. However, the age of the best 25% of cars cannot be determined with the given information.

To draw a model for auto fuel economy, we need to use the given mean and standard deviation. The model can be represented by a normal distribution curve, with the mean as the center and the standard deviation as a measure of spread. In this case, the mean is 272 mg and the standard deviation is 58 mg per gallon.

In the 68-95-99.7 rule, we expect the majority of the data to be within one standard deviation from the mean. Therefore, we can expect the fuel economy to be between 214 mg/gal and 330 mg/gal with about 68% confidence.

If we assume a normal distribution and use the 68-95-99.7 rule, we can estimate that about 16% of autos should get more than 330 mg/gal. This can be calculated by subtracting the cumulative probability at 330 mg/gal from 1.

Considering bad fuel economy as less than 214 mg/gal, we can estimate that approximately 16% of autos should get bad gas mileage based on the 68-95-99.7 rule.

The age of the best 25% cars is not provided in the given information, so it cannot be accurately determined.

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