Chapter 6, Problem 34E

a)

To determine

To find the values that should border the middle 95% of all car speeds.

Answer to Problem 34E

The 95% of all car speeds should be between 16.72 mph and 30.96 mph.

Explanation of Solution

Given:

  $\mu$ = 23.84

  $\sigma$ = 3.56

  

As per rule of 68-95-99.7, 95% of all the data should be lie within 2 standard deviations from the mean.

Therefore,

  $\begin{array}{l}\mu -2\sigma =23.84-2\times 3.56=16.72\\ \mu +2\sigma =23.84+2\times 3.56=30.96\end{array}$

Using Normal model, the 95% of all car speeds should be between 16.72 mph and 30.96 mph.

b)

To determine

To explain how well does model in predicting percentiles.

Answer to Problem 34E

Well.

Explanation of Solution

Given:

  $\mu$ = 23.84

  $\sigma$ = 3.56

  

Using Normal model, the 95% of all car speeds should be between 16.72 mph and 30.96 mph.

In given summary statistic, the middle 95% are between 16.638 mph and 30.976 mph. Therefore, the predicted values and given values are almost close. Hence, the model does well in predicting the percentiles.