Chapter 3: Q. 124 (page 231)

Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) that are female is 48.60. Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over. Of
the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.
Suppose that 10,000 U.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

Expert verified

a. $P (M) = 0.514$

	<20	20–64	>64	Totals
Female	0.0244	0.3954	0.0661	0.486
Male	0.0259	0.4186	0.0695	0.514
Totals	0.0503	0.814	0.1356	1

c. $P (F 20 - 64) = 0.4857$

Step by step solution

Given information

The percent of licensed U.S. drivers (from a recent year) that are female is 48.60.

Of the females, 5.03% are age 19 and under; 81.36% are age 20–64; 13.61% are age 65 or over.

Of the licensed U.S. male drivers, 5.04% are age 19 and under; 81.43% are age 20–64; 13.53% are age 65 or over.

(part a)

The male drivers are randomly selected and the probability is given by

$P (M) = 0.514$

Explanation (part b)

a contingency table of gender versus age group is given by

	<20	20–64	>64	Totals
Female	0.0244	0.3954	0.0661	0.486
Male	0.0259	0.4186	0.0695	0.514
Totals	0.0503	0.814	0.1356	1

Explanation (part c)

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

	<20	20–64	>64	Totals
Female	0.0244	0.3954	0.0661	0.486
Male	0.0259	0.4186	0.0695	0.514
Totals	0.0503	0.814	0.1356	1

$P (F 20 - 64) = \frac{T o t a l n u m b e r o f f e m a l e d r i v e r s i n a g e 20 - 64}{t o t a l n u m b e r o f d r i v e r s i n a g e 20 - 64} P (F 20 - 64) = \frac{0.3954}{0.814} P (F 20 - 64) = 0.4857$

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Short Answer

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Given information

(part a)

Explanation (part b)

Explanation (part c)

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