Question

environmental protection agency (epa) fuel economy estimates for automobile models tested recently predicted a mean of 24.81 mpg. assume that a normal model can be applied. use the 68 - 95 - 99.7 rule to complete parts a through e.

b) in what interval would you expect the central 95% of autos to be found?
using the 68 - 95 - 99.7 rule, the central 95% of autos can be expected to be found in the interval from 12.37 to 37.25 mpg. (type integers or decimals. do not round. use ascending order.)

c) about what percent of autos should get more than 31.03 mpg?
using the 68 - 95 - 99.7 rule, about 16 % of autos should get more than 31.03 mpg. (type an integer or a decimal. do not round.)

d) about what percent of autos should get between 31.03 and 37.25 mpg?
using the 68 - 95 - 99.7 rule, about 13.5 % of autos should get between 31.03 and 37.25 mpg. (type an integer or a decimal. do not round.)

e) describe the gas mileage of the worst 2.5% of cars.
the worst 2.5% of cars get than mpg. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall 68 - 95 - 99.7 Rule

In a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean, 95% within 2 standard - deviations, and 99.7% within 3 standard - deviations. The normal distribution is symmetric about the mean.

Step2: Analyze part e

The central 95% of the data lies within 2 standard - deviations of the mean. So, the remaining 5% is split evenly between the two tails (2.5% in the lower tail and 2.5% in the upper tail).
We know from part b that the interval for the central 95% is from 12.37 to 37.25 mpg. The lower 2.5% of the data is below 12.37 mpg.

Answer:

The worst 2.5% of cars get less than 12.37 mpg.