Simulation and Random Number Generation for AP Statistics (page 2)

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By — McGraw-Hill Professional
Updated on Feb 3, 2011

The following represents a few trials of this simulation (actually done using the random number generator on the TI-83/84 calculator):

This limited simulation shows that the number of boys and girls in the population are equal. In fairness, it should be pointed out that you usually won't get exact results in a simulation such as this, especially with only 15 trials, but this time the simulation gave the correct answer: the behavior would not change the proportion of girls in the population.

The following gives 200 outcomes of a typical random number generator separated into groups of 5 digits:

    example: A coin is known to be biased in such a way that the probability of getting a head is 0.4. If the coin is flipped 50 times, how many heads would you expect to get?
    solution: Let 0, 1, 2, 3 be a head and 4, 5, 6, 7, 8, 9 be a tail. If we look at 50 digits beginning with the first row, we see that there are 18 heads (bold-faced below), so the proportion of heads is 18/50 = 0.36. This is close to the expected value of 0.4.
    79692 51707 73274 12548 91497 11135 81218 79572 06484 87440

Sometimes the simulation will be a wait-time simulation. In the example above, we could have asked how long it would take, on average, until we get five heads. In this case, using the same definitions for the various digits, we would proceed through the table until we noted five even numbers. We would then write down how many digits we had to look at. Three trials of that simulation might look like this (individual trials are separated by \\):

    79692 51707 732\\74 12548 91497 11\\135 8121\\.

So, it took 13, 14, and 7 trials to get our five heads, or an average of 11.3 trials (the theoretical expected number of trials is 12.5).

Remember that you will not be able to use these functions to do a required simulation on the AP exam, although you can use them to do a simulation of your own design.

Practice problems for these concepts can be found at:

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