EXAMPLE 11 Probability models based on frequency tables

Table 2 contains the employment type for a sample of 1000 employed citizens of Fairfax County, Virginia.3 Use the data to construct the probability model by generating the relative frequencies and using the relative frequencies to estimate the probabilities for each employment type.

Table 5.9: Table 2 Employment types
Employment type Count
Private company 597
Federal government 141
Self-employed 97
Private nonprofit 92
Local government 59
State government 12
Other 2

251

Solution

We calculate the relative frequencies of each employment group by dividing the count (frequency) for each group by the sample size 1000. For example, the relative frequency for “Private Company” is . The relative frequency is then used to estimate the probability of selecting citizens who work at private companies in Fairfax County, Virginia. Filling in the remaining calculations produces the probability model in Table 3. Note that the table follows the Rules of Probability in that (a) each outcome has probability between 0 and 1, and (b) the sum of the probabilities of all the outcomes equals 1.0.

Table 5.10: Table 3 Probability model
Employment type Probability
Private company 0.597
Federal government 0.141
Self-employed 0.097
Private nonprofit 0.092
Local government 0.059
State government 0.012
Other 0.002

fairfaxemploy

NOW YOU CAN DO

Exercises 61 and 62.