Question

a) draw the model for auto fuel economy. clearly label it, showing what the 68 - 95 - 99.7 rule predicts.
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 % of autos should get more than 31.03 mpg. (type an integer or a decimal. do not round.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean, about 95% lies within 2 standard - deviations of the mean, and about 99.7% lies within 3 standard - deviations of the mean.

Step2: Analyze part (c)

We know that the total area under the normal curve is 100%. If the central 95% of the data lies within 2 standard - deviations of the mean, then the remaining area outside of this interval is \(100 - 95=5\%\). This 5% is split evenly between the two tails. So the area in the right - hand tail (values greater than 2 standard - deviations above the mean) is \(\frac{5}{2}=2.5\%\).

Answer:

2.5