Question

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. Part (a) How many drivers would you expect to be male? drivers Part (b) Using a tree diagram of the given situation, construct a contingency table of gender versus age group. (Round your answers to the nearest whole number.) 19 and under 20-64 65 and over Total Female Male Total 10,000 Part (c) Using the contingency table, find the probability that out of the age 20-64 group, a randomly selected driver is female.

Answer 1

a. We would expect approximately 5,140 drivers to be male.

b. The contingency table is attached as image

c. The probability that a randomly selected driver from the age group 20-64 is female is approximately 0.500 or 50%.

How to determine the number of drivers expected to be male

(a) To determine the number of drivers expected to be male, multiply the total number of drivers (10,000) by the percentage of licensed U.S. drivers that are male.

Number of male drivers = 10,000 * (1 - 0.4860) ≈ 5,140

Therefore, we would expect approximately 5,140 drivers to be male.

(b) The contingency table can be constructed using the given percentages and the total number of drivers (10,000).

Note: The totals for each category may slightly deviate due to rounding.

(c) To find the probability that a randomly selected driver from the age group 20-64 is female, divide the number of female drivers in that age group by the total number of drivers in the age group 20-64.

Probability = Female drivers in age group 20-64 / Total drivers in age group 20-64

Probability = 8,136 / 16,279 ≈ 0.500

Therefore, the probability that a randomly selected driver from the age group 20-64 is female is approximately 0.500 or 50%.