# Probabilities of being in certain age categories

Topic 18 Exp 3

The following table contains information on the 2002 resident population of

the U.S., by age. (Source: The New York Times Almanac 2004, page 277.)

================================================================================ Younger

Age than 18

years old 18 to 24 25 to 44 45 to 64 65 years and older

Number (in Thousands 1,107,108 452,196 1,270,419 1,068,243 588,542

================================================================================

(a). If a resident of the U.S. is chosen at random, find the probability that he or she is 25 to 44 years old.

(b). If a resident is chosen at random, find the probability that he or she is older than 24 years old.

(c). In what age category does the median age fall?

See attached worksheet. Could you please use the steps you used (equations etc.) when solving the problem?

#### Solution Preview

One of the keys to solving this problem is to consider the FRACTIONS of U.S. residents in various age categories. To get those fractions, one thing we need to do is compute the TOTAL number of U.S. residents (regardless of age category).

The total number of U.S. residents is the sum of the numbers of U.S. residents in the five individual age categories, so we will first compute that sum:

1,107,108

452,196

1,270,419

1,068,243

+ 588,542

______________

4,486,508

Each of these numbers is in units of A THOUSAND, so the actual number of U.S. residents is 1,000 TIMES 4,486,508, but we won't actually need to perform that multiplication in order to solve this problem.

(a) The probability that a U.S. resident chosen at random is 25 to 44 years old is the ratio of the number of U.S. residents in that age category (1,270,419) to the TOTAL number of U.S. residents (4,486,508). [Both of the numbers in that ratio would have to be multipied by 1000 to get the ACTUAL numbers, but when their RATIO is computed, that extra factor of 1000 in the NUMERATOR will CANCEL the extra factor of 1000 in the DENOMINATOR, so the answer will be correct WITHOUT multiplying the numbers by 1000.]

The probability that a U.S. resident chosen at random is 25 to ...

#### Solution Summary

The probabilities that are to be found in parts (a) and (b), and the age category that is to be found in part (c), have been computed and are accompanied by detailed explanations.