AP STATISTICS LESSON 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 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. 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). 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. Choose a person at random from a group of which 70% are employed. One digit simulates one person. For example: For example: 0, 1, 2, 3, 4, 5, 6 = employed 7, 8, 9 = not employed 7, 8, 9 = not employed Note: Other numeric assignments may be used but always try to use the most efficient set. 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: Choose one person at random from a group of 73% are employed. Now two digits simulate one person: For example: For example: 00, 01, 02,...., 72 = employed 73, 74, 75,...., 99 = not employed 73, 74, 75,...., 99 = not employed

Assigning Digits Example 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: 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 5, 6 = unemployed 7, 8, 9 = not in the labor force 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, 6.12Exercises 6.1, 6.2, 6.7, 6.12 Follow our 4-step processFollow our 4-step process

Tonight Complete Exercise 6.20 (Due tomorrow) Keep reading, make a note of questions Watch video lectures Start WebAssign Bring your textbooks tomorrow.

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