Question

Suppose that $10,000U.S.$licensed drivers are randomly selected.

a. How many would you expect to be male?

b. Using the table or tree diagram, construct a contingency table of gender versus age group.

c. Using the contingency table, find the probability that out of the age $20-64$group, a randomly selected driver is female.

Short answer

(a) In $10000$people, $5140$are male.

(b) The contingency table of gender versus age is given below.

(c) The probability that out of the age $20-64$age, the randomly selected driver is female is $0.486$

Step-by-step solution

Find the no. of male (part a)

Female drivers account for $48.6\%$of all drivers. $5.03\%$are under the age of $19$, $81.36\%$are between the ages of $20$and $64$, and $13.61\%$are $65$and older.

When it involves to male drivers, $5.04\%$are aged $19$and under, $81.43\%$are aged $20-64$, and $13.53\%$are aged $65$and under.

We have $10000$drivers who were chosen every which way.

If $48.6\%$of the drivers are projected to be female, $51.4$percent of the drivers are predicted to be male. As a result, if we had$10000$persons, we anticipate that

$\frac{51.4}{100}10000=5140$of them are male.

Using table, find the gender versus people (part b)

There are $4860$female drivers for$5140$male drivers.

Let's break down girls into age groups.

$5.03\%$of them are under the age of$19$:

$\frac{5.03}{100}4860=244.458$

$$\begin{gathered} =0.0503\times 0.486 \\ =0.02445 \\ =2.445\% \end{gathered}$$

$81.36$percent of peoples are $20-64$:

$\frac{81.36}{100}4860=3951.18$

$$\begin{gathered} 0.8136\times 0.486 \\ =0.3954 \\ =39.54\% \end{gathered}$$

$13.61\%$of them are $65$and above:

$\frac{13.61}{100}4860=661.446$

$$\begin{gathered} =0.1361\times 0.486 \\ =0.0661 \\ =6.61\% \end{gathered}$$

Now, we calculate females by age:

$5.04$percent of females are $19$and under:

$\frac{5.04}{100}5140=259.056$

$$\begin{gathered} =0.0504\times 0.514 \\ =0.0259 \\ =2.59\% \end{gathered}$$

$81.43\%$of them are $20-64$:

$\frac{81.43}{100}5140=4185.502$

$$\begin{gathered} =0.8143\times 0.514 \\ =0.4186 \end{gathered}$$

$13.53\%$are $65$and above:

$\frac{13.53}{100}5140=695.442$

$$\begin{gathered} =0.1353\times 0.514 \\ =0.1256 \\ =13.56\% \end{gathered}$$

Table diagram (part b)

Table diagram for number of peoples:

	<20	20-64	>64	Total
female	244.458	3951.18	661.446	4860
male	259.056	4185.502	695.442	5140
Total	503.514	8136.682	1356.888	10000

Table diagram for percentage:

	<20	20-64	>64	Total
female	0.0244	0.3954	0.0661	0.486
male	0.0259	0.4186	0.0695	0.514
Total	0.0503	0.814	10.1356	1

find the probability that between age 20-64 (part c)

Probability that between the age $20-64$,

$$\begin{gathered} P=\frac{0.3954}{0.814} \\ =0.486 \end{gathered}$$