EXAMPLE 2 Assigning digits for simulation

In the United States, the Age Discrimination Employment Act (ADEA) forbids age discrimination against people who are age 40 and over. Terminating an “unusually” large proportion of employees age 40 and over can trigger legal action. Simulation can help determine what might be an “unusual” pattern of terminations. How might we set up such a simulation?

  1. (a) Choose one employee at random from a group of which 40% are age 40 and over. One digit simulates one employee:

    0, 1, 2, 3 = age 40 and over

    4, 5, 6, 7, 8, 9 = under age 40

  2. (b) Choose one employee at random from a group of which 43% are age 40 and over. Now two digits simulate one person:

    00, 01, 02, . . . , 42 = age 40 and over

    43, 74, 75, . . . , 99 = under age 40

    We assigned 43 of the 100 two-digit pairs to “age 40 and over” to get probability 0.43. Representing “age 40 and over” by 01, 02, . . . , 43 and “under age 40” by 44, 45, . . . , 99, 00 would also be correct.

    450

  3. (c) Choose one employee at random from a group of which 30% are age 40 and over and have no plans to retire, 10% are age 40 and over and plan to retire in the next few months, and 60% are under age 40. There are now three possible outcomes, but the principle is the same. One digit simulates one person:

    0, 1, 2 = age 40 and over and have no plans to retire

    3 = age 40 and over and plan to retire in the next few months

    4, 5, 6, 7, 8, 9 = under age 40