Chapter 4.1, Problem 15E

To determine

a)

To find:

The experimental probability.

Answer to Problem 15E

Solution:

The probability that the next respondent selected by the telemarketer’s computer will be over 45 years of age is 0.2914.

Explanation of Solution

Given:

The table is given as,

Number of Respondents by Age
18-25	26-35	36-45	Over 45
29	40	55	51

Formula used:

Let E denote the event that the selected respondent is over 45 years of age. Then, $P\left(E\right)$ denotes the probability that E occurs. The probability is given by,

$P\left(E\right)=\frac{f}{n}$

Where, f denotes the frequency of the event E and n denotes the number of times the experiment is repeated.

Calculation:

In this case, f denotes the number of respondents of age over 45 years and n denotes the total number of respondents selected. From the table,

$\begin{array}{l}f=51\hfill \\ n=29+40+55+51=175\hfill \end{array}$

Thus, the probability that the next respondent selected will be over 45 years of age is given by,

$\begin{array}{rll}P\left(E\right)& =& \frac{f}{n}\\ & =& \frac{51}{175}\\ & =& 0.2914\end{array}$

To determine

b)

To find:

The experimental probability.

Answer to Problem 15E

Solution:

The probability that the next respondent selected by the telemarketer’s computer will be aged between 26 and 35 years is 0.2286.

Explanation of Solution

Given:

The table is given as,

Number of Respondents by Age
18-25	26-35	36-45	Over 45
29	40	55	51

Formula used:

Let E denote the event that the selected respondent is aged between 26 and 35 years. Then, $P\left(E\right)$ denotes the probability that E occurs. The probability is given by,

$P\left(E\right)=\frac{f}{n}$

Where, f denotes the frequency of the event E and n denotes the number of times the experiment is repeated.

Calculation:

In this case, f denotes the number of respondents of age between 26 - 35 and n denotes the total number of respondents selected. From the table,

$\begin{array}{l}f=40\hfill \\ n=29+40+55+51=175\hfill \end{array}$

Thus, the probability that the next respondent selected will be aged between 26-35 years is given by,

$\begin{array}{rll}P\left(E\right)& =& \frac{f}{n}\\ & =& \frac{40}{175}\\ & =& 0.2286\end{array}$

To determine

c)

To find:

The experimental probability.

Answer to Problem 15E

Solution:

The probability that the next respondent selected by the telemarketer’s computer will be at least 36 years in age is 0.6057.

Explanation of Solution

Given:

The table is given as,

Number of Respondents by Age
18-25	26-35	36-45	Over 45
29	40	55	51

Formula used:

Let E denote the event that the selected respondent is at least 36 years of age. Then, $P\left(E\right)$ denotes the probability that E occurs. The probability is given by,

$P\left(E\right)=\frac{f}{n}$

Where, f denotes the frequency of the event E and n denotes the number of times the experiment is repeated.

Calculation:

In this case, f denotes the number of respondents of age at least 36 years and n denotes the total number of respondents selected. From the table, a respondent at least 36 years of age will either belong to the interval ’36-45’ or ‘Over 45’. So,

$\begin{array}{l}f=55+51=106\hfill \\ n=29+40+55+51=175\hfill \end{array}$

Thus, the probability that the next respondent selected will be at least 36 years of age is given by,

$\begin{array}{rll}P\left(E\right)& =& \frac{f}{n}\\ & =& \frac{106}{175}\\ & =& 0.6057\end{array}$