AP STATISTICSLESSON 6-1

Simulation

ESSENTIAL QUESTION:

How can simulation be used to solve problems involving chance?

Objectives:

To simulate problems of chance with the help of a random number table.

To simulate problems of chance using the calculator.

Three methods of simulation to answer questions involving

chance.

1. Try to estimate the likelihood of a result by actually carrying out the experiment.

2. Develop a probability model and use it to calculate a theoretical answer.

3. Start with a model that, in some fashion, reflects the truth about the experiment, and then develop a procedure for simulating of repetitions of the experiment.

Simulation

The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration, is called a simulation.

Independent (trials) – One event has no effect or influence over the next (e.g. coin tosses).

Simulation Steps

State: State the problem or describe the experiment.

Plan: State the assumptions & assign digits to represent outcomes. Clearly explain

how to identify the outcomes and what variables to measure.

Do: Simulate many repetitions.

Conclude: Use the results of your simulation to answer the question of interest.

Assigning Digits

Example 6.4A

Choose a person at random from a group of which 70% are employed. One digit simulates one person.

For example:0, 1, 2, 3, 4, 5, 6 = employed

7, 8, 9 = not employed

Note: Other numeric assignments may be used but always try to use the most efficient set.

Assigning Digits

Example 6.4B

Choose one person at random from a group of 73% are employed. Now two digits simulate one person:

For example:

00, 01, 02, . . . . , 72 = employed

73, 74, 75, . . . . , 99 = not employed

Assigning DigitsExample 6.4C

Choose one person at random form a group of which 50% are employed, 20% are unemployed, and 30% are not in the labor force. There are now three possible outcomes, but the principle is the same. One digit simulates one person:

For example:0, 1, 2, 3, 4 = employed

5, 6 = unemployed 7, 8, 9 = not in the labor force

Example 6.6

A couple plans to have children until they have a girl or until they have four children, whichever comes first. We want to estimate the likelihood that they will have a girl.

State:

Plan:

Do:

Conclude:

Simulation with the calculator

Step 1: Press “Math” button

Step 2: Press right arrow “” twice and highlight Prob.

Step 3: Press “5” randint

Step 4: Enter beginning number, ending number, and the number of values to be chosen

at a time.

Your turn…

• Exercises 6.1, 6.2, 6.7, 6.12• Follow our 4-step process

Tonight

Complete Exercise 6.20 (Due tomorrow)

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