Transcript A P STATISTICS LESSON 5 - 3

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 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 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:
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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