Question

fuel economy estimates for automobiles built one year predicted a mean of 25.8 mpg and a standard deviation of 6.2 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.

b) in what interval would you expect the central 99.7% of autos to be found?

using the 68 - 95 - 99.7 rule, the central 99.7% of autos can be expected to be found in the interval from

to

mpg.

(do not round. type integers or decimals.)

Explanation:

Step1: Recall the 68 - 95 - 99.7 Rule

The 68 - 95 - 99.7 Rule for a normal distribution states that approximately 99.7% of the data lies within \( \mu\pm3\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Calculate the lower and upper bounds

Given \(\mu = 25.8\) mpg and \(\sigma=6.2\) mpg.
The lower bound is \(\mu - 3\sigma\).

$$
LATEXBLOCK0
$$

The upper bound is \(\mu + 3\sigma\).

$$
LATEXBLOCK1
$$

Answer:

7.2 to 44.4