Chapter 2, Problem 44E

a)

To determine

Identify the sample mean number of minutes late.

Explanation of Solution

From the given information, the mean number of claims per policy can be calculated as follows:

$\begin{array}{c}\text{Mean}\left(\overline{\text{X}}\right)=\frac{{{\displaystyle \sum {\text{m}}_{\text{i}}\text{f}}}_{\text{i}}}{\text{n}}\\ =\frac{1505}{83}\\ =18.1325\end{array}$

A table can be constructed using the value of mean as follows:

Table 1.

mi	fi	${\text{f}}_{\text{i}}{\text{m}}_{\text{i}}$	$\left({\text{m}}_{\text{i}}-\overline{\text{X}}\right)$	${\left({\text{m}}_{\text{i}}-\overline{\text{X}}\right)}^2$	${\text{f}}_{\text{i}}{\left({\text{m}}_{\text{i}}-\overline{\text{X}}\right)}^2$
5	30	150	-13.133	172.46	5173.90
15	25	375	-3.133	9.81	245.32
25	13	325	6.867	47.16	613.11
35	6	210	16.867	284.51	1707.07
45	5	225	26.867	721.86	3609.30
55	4	220	36.867	1359.21	5436.84
Total	83	1505			16785.54

b)

To determine

Identify the sample variance and standard deviations.

Explanation of Solution

The sample variance and standard deviation can be calculated using the tabulated values as follows:

$\begin{array}{c}\text{Sample varience }\left({\text{S}}^2\right)=\frac{{\displaystyle \sum {\text{f}}_{\text{i}}{\left({\text{m}}_{\text{i}}-\overline{\text{X}}\right)}^2}}{\text{n}-1}\\ =\frac{16785.54}{82}\\ =204.7017\\ \text{Standard deviation}\left(\text{S}\right)=\sqrt{204.7017}\\ =14.307\end{array}$