Chapter 8.6, Problem 54E

a.

To determine

To estimate: the number of unemployed workers in the 16-19 age group.

Answer to Problem 54E

The number of unemployed workers in the 16-19 age group is 0.8376 million.

Explanation of Solution

Given information: There were approximately 6.98 million unemployed workers in the

U.S. The below circle graph shows the age profile of these unemployed workers.

  

Calculation:

The total number of unemployed workers $\approx$ 6.98 million.

From the graph the number of unemployed workers in the 16-19 age group=12% of 6.98.

The number of unemployed workers in the 16-19 age group,

  $=\frac{12}{100}\times 6.98=0.8376$ million.

b.

To determine

To estimate: the number of unemployed workers who are 45 years or older.

Answer to Problem 54E

The number of unemployed workers who are 45 years or older is 2.2336 million.

Explanation of Solution

Given information: There were approximately 6.98 million unemployed workers in the

U.S. The below circle graph shows the age profile of these unemployed workers.

  

Calculation:

The total number of unemployed workers $\approx$ 6.98 million.

From the graph the number of unemployed workers who are 45 years or older= 45-54 year group+ 55-64 year group +65 and older year group=15%+12%+5%=32% of 6.98.

The number of unemployed workers who are 45 years or older,

  $=\frac{32}{100}\times 6.98=2.2336$ million

c.

To determine

To find: the probability that a person selected at random from the population of unemployed workers is in the 25-44 age group.

Answer to Problem 54E

The probability that a person selected at random from the population of unemployed workers is in the 25-44 age group is 0.4.

Explanation of Solution

Given information: There were approximately 6.98 million unemployed workers in the

U.S. The below circle graph shows the age profile of these unemployed workers.

  

Calculation:

The total number of unemployed workers $\approx$ 6.98 million.

From the graph the number of unemployed workers is in the 25-44 age group=25-34 age group + 35-44 age group=24%+16%=40% of 6.98.

So, the number of unemployed workers is in the 25-44 age group,

  $=\frac{40}{100}\times 6.98=2.792$ million.

The probability that a person selected at random from the population of unemployed workers is in the 25-44 age group=(number of unemployed workers is in the 25-44 age group/total number of unemployed workers).

The probabilityof unemployed workers is in the 25-44 age group $=\frac{2.792}{6.98}=0.4$ .

d.

To determine

To find: the probability that a person selected at random from the population of unemployed workers is in the 25-64 age group.

Answer to Problem 54E

The probabilityof unemployed workers is in the 25-64 age group is 0.67.

Explanation of Solution

Given information: There were approximately 6.98 million unemployed workers in the

U.S. The below circle graph shows the age profile of these unemployed workers.

  

Calculation:

The total number of unemployed workers $\approx$ 6.98 million.

From the graph the number of unemployed workers is in the 25-64 age group=25-34 age group + 35-44 age group+45-54 age group +55-64 age group ,

= 24%+16%+15%+12%=67% of 6.98.

So, the number of unemployed workers is in the 25-64 age group,

  $=\frac{67}{100}\times 6.98=4.6766$ million.

The probability that a person selected at random from the population of unemployed workers is in the 25-64 age group=(number of unemployed workers is in the 25-64 age group/total number of unemployed workers).

The probabilityof unemployed workers is in the 25-64 age group $=\frac{4.6766}{6.98}=0.67$ .