Use the following information to answer the next two exercises. The percent of l

Question

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.

Explanation / Answer

There are three groups for female licensed U.S. drivers and three groups for males as well.

F1 = females of or under age 19 , F2 = females within age 20-64 ; F3= females of or above ae 65 .

Similarly,

M1=males of or under age 19 , M2= males aged between 20-64 , M3= males of or above age 65.

Now, we have in percent 48.60 are female licensed driver , So, 100-48.6 = 51.4 % of drivers( from now onwards drivers will resemble here as licensed driver) are male .

(a) So we expect 51.4*10000/100 = 5140 males among 10000 drivers [ By simple unitary method ]

(b) The Contingency Table that shows the distribution of age classes and gender is as follows,

                                     Gender

Age groups

(48.60*5.03*10000)/100

=244.458

(51.4*5.04*10000/100)

=259.056

20-64

(48.60*81.36*10000)/100

=3954.096

(51.4*81.43*10000)/100

=4185.502

(48.60*13.61*10000)/100

=661.446

(51.4*13.53*10000)/100

=695.442

Now here out of all the drivers 8139.598 are between 20-64 age.

Now the probability that a chosen driver will be a female when randomly chosen from a driver within age group 20-64 is ,

(3954.096/8139.598)= 0.4857852.

                                     Gender

Age groups

Female Male Total equal to OR under 19

(48.60*5.03*10000)/100

=244.458

(51.4*5.04*10000/100)

=259.056

503.514

20-64

(48.60*81.36*10000)/100

=3954.096

(51.4*81.43*10000)/100

=4185.502

8139.598 equal to OR above 65

(48.60*13.61*10000)/100

=661.446

(51.4*13.53*10000)/100

=695.442

1356.888 Total 4860 5140 10000

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