Transcript 5-3 Day 1

AP STATISTICS
LESSON 5 - 3
SIMULATING EXPERIMENTS
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
Step 1: State the problem or describe the
experiment.
Step 2: State the assumptions.
Step 3: Assign digits to represent outcomes.
Step 4: Simulate many repetitions.
Step 5: State your conclusions.
Assigning Digits
Example A
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 B
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 C
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
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: Press first digit of series, hit comma, then
hit number in population, hit the comma button
and finally place the number at a time that you
want. Close parenthesis.