Chapter 9.7, Problem 35E

a.

To determine

Find the number of unemployed workers.

Answer to Problem 35E

  $0.996\text{ million}$

Explanation of Solution

Calculation:

In $\text{2}0\text{15}$ , there were approximately $\text{8}.\text{3}$ million unemployed workers in the United States. The circle graph shows the age profile of these unemployed workers.

  

To estimate the number of unemployed workers in the $\text{16}–\text{19}$ age group,

Consider,

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

From the pie chart, the percentage of unemployed workers in the $\text{16}–\text{19}$ age group is $12\%$ .

Total number of unemployed workers $\text{=8}\text{.3 million}$

So, approximate number of unemployed workers in that age-group is,

  $\begin{array}{l}\text{=12\% of 8}\text{.3 million}\\ =\frac{12}{100}\times 8.3\\ =0.996\text{ million}\end{array}$

Hence, approximate number of unemployed workers in that age-group is $0.996\text{ million}$ .

b.

To determine

Find the probability that a person selected at random.

Answer to Problem 35E

  $0.18$

Explanation of Solution

Calculation:

In $\text{2}0\text{15}$ , there were approximately $\text{8}.\text{3}$ million unemployed workers in the United States. The circle graph shows the age profile of these unemployed workers.

  

To estimate the number probability that a person selected at random from the population of unemployed workers is in the $\text{2}0–\text{24}$ age group

Consider,

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

From the pie chart, the percentage of unemployed workers in the $\text{2}0–\text{24}$ age-group

is $18\%$ .

Total number of unemployed workers $\text{=8}\text{.3 million}$

So, probability that a person selected at random from the population of unemployed workers is in the $\text{2}0–\text{24}$ age group is,

  $=\frac{\text{\%age of unemployed workers in 20-24 age-group}}{\text{total \%age of unemployed workers}}$

  $\begin{array}{l}=\frac{18}{100}\\ =0.18\end{array}$

Hence, approximate number of unemployed workers in that age-group is $0.18$ .

c.

To determine

Find the probability that a person selected at random.

Answer to Problem 35E

  $0.54$

Explanation of Solution

Calculation:

In $\text{2}0\text{15}$ , there were approximately $\text{8}.\text{3}$ million unemployed workers in the United States. The circle graph shows the age profile of these unemployed workers.

  

To estimate the number probability that a person selected at random from the population of unemployed workers is in the $\text{25}–\text{54}$ age group,

Consider,

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

From the pie chart, the percentage of unemployed workers in the $\text{25}–\text{54}$ age group is $54\%$ .

Total number of unemployed workers $\text{=8}\text{.3 million}$

So, probability that a person selected at random from the population of unemployed workers is in the $\text{25}–\text{54}$ age group is,

  $=\frac{\text{\%age of unemployed workers in 25-54 age-group}}{\text{total \%age of unemployed workers}}$

  $\begin{array}{l}=\frac{54}{100}\\ =0.54\end{array}$

Hence, approximate number of unemployed workers in that age-group is $0.54$ .

d.

To determine

Find the probability that a person selected at random.

Answer to Problem 35E

  $0.16$

Explanation of Solution

Calculation:

In $\text{2}0\text{15}$ , there were approximately $\text{8}.\text{3}$ million unemployed workers in the United States. The circle graph shows the age profile of these unemployed workers.

  

To estimate the number probability that a person selected at random from the population of unemployed workers is in $\text{55}$ or older,

Consider,

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

Probability of two mutually exclusive events: $P\left(E\right)=P\left(A\right)+P\left(B\right)$

From the pie chart, the percentage of unemployed workers in the $55-64$ age group is $\text{12\%}$ and $65$ or older is $\text{4\%}$ .

Total number of unemployed workers $\text{=8}\text{.3 million}$

So, probability that a person who is $\text{55}$ or older is,

  $=\frac{\text{\%age of unemployed workers in 55-60 age-group+\%age of unemployed workers in 65 or older}}{\text{total \%age of unemployed workers}}$

  $\begin{array}{l}=\frac{12+4}{100}\\ =0.16\end{array}$

Hence, approximate number of unemployed workers in that age-group is $0.16$ .