Chapter PI, Problem 27RE

(a)

To determine

To plot these data.

Explanation of Solution

It is given in the question the list of number of pieces of mail received at a school office. Thus, the plot of this data will be as:

(b)

To determine

To find appropriate summary statistics.

Answer to Problem 27RE

  $\begin{array}{l}\text{Mean}=100.25\text{pieces of mail}\\ \text{Standard deviation}=25.54\text{ pieces of mail}\end{array}$

Explanation of Solution

It is given in the question the list of number of pieces of mail received at a school office. Thus, the appropriate summary statistics will be calculated through the calculator $\text{TI}-89$ . Thus, if we have to compute the summary statistics then press $\text{F4}$ , that is Calc. and then input the name of the list using VAR-LINK and then press enter. The summary statistics will appear/ thus, the result will be:

  $\begin{array}{l}\text{Mean}=100.25\text{pieces of mail}\\ \text{Standard deviation}=25.54\text{ pieces of mail}\end{array}$

(c)

To determine

To write a brief discussion of the school’s mail deliveries.

Explanation of Solution

It is given in the question the list of number of pieces of mail received at a school office. Thus, as we look at the histogram of the data we can say that the distribution is somewhat symmetric in nature as the shape of the histogram appears to be bell-shaped. And the distribution appears to be uni-modal but the centre is rather flat and almost uniform in nature.

(d)

To determine

To find out what percentage of days actually lie within one standard deviation of the mean.

Answer to Problem 27RE

  $64\%$ .

Explanation of Solution

It is given in the question the list of number of pieces of mail received at a school office. Thus, as we look at the histogram of the data we can say that the distribution is somewhat symmetric in nature. Thus, the percentage of days actually lie within one standard deviation of the mean is $64\%$ . The normal model seems to work perfectly well since it predicts $68\%$ .