5.63 Simulating arrivals to local holiday center The director of a local holiday center is offering a special prize to the first married visitor. The distribution of the marital status for Americans estimated by SDA (Survey Documentation and Analysis) is shown below:

The director decides that if more than 20 visitors are required before the first married visitor arrives, she will need to issue a special advertisement for married people.

a. Conduct a simulation 10 times, using the Random Numbers app accessible on the book’s website or a calculator or a software, to estimate the probability this will happen. Show all steps of the simulation, including any assumptions that you make. Refer to Example 16 as a model for carrying out this simulation.

b. In practice, you would do at least 1000 simulations to estimate this probability well. You’d then find that the probability of exceeding 20 visitors before finding a married visitor is 0.36. Actually, simulation is not needed. Show how to find this probability by using the methods of this chapter.

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Marital Married Widowed Divorced Separated Did not Status marry Probability 53.60% 9.70% 12.60% 3.50% 20.60%