SimulationsHow many boxes does it take to get

a complete set of pictures of Tiger Woods, Lance Armstrong, and Serena Williams if the manufacturer of the cereal randomly put 20% Tiger, 30% Lance and 50% Serena pictures in the cereal boxes?

Vocabulary

• Simulation

• Components

• Trial

Steps for making a simulation1. Identify the component to be repeated

2. Explain how you will model the outcome

3. Explain how you will simulate the trial.

4. State clearly what the response variable is.

5. Run several trials.

6. Analyze the response variable.

7. State your conclusion in context.

The Simulation

• The simulation:– how many boxes do I need to buy to get at how many boxes do I need to buy to get at

least one picture of each?least one picture of each?

Steps for making a simulation

1. Identify the component to be repeated,

the situation that is repeated

““selecting a box of cereal box”selecting a box of cereal box”

Steps for making a simulation2. Explain how you will model the outcome

think of a set of numbers where 20% of them represent Tiger, 30% Lance, and 50% Serena.

use 0-9 where use 0-9 where

0-4 = Serena 0-4 = Serena

5-7 = Lance 5-7 = Lance

8-9 = Tiger8-9 = Tiger

Steps for making a simulation3. Explain how you will simulate the trial.

a trial is a series of components until the desired goal is achieved.

““opening boxes until we have one of opening boxes until we have one of each”each”

selecting a random number from a selecting a random number from a random number list until we have at least random number list until we have at least one number from each group.one number from each group.

0-4 0-4 and 5-7 5-7 and 8-9 8-9

Steps for making a simulation4. State clearly what the response variable is.

what are we interested in?

““how many boxes will it take to get 1 how many boxes will it take to get 1 picture of each?”picture of each?”

response variable = # of random digits response variable = # of random digits until you have one from each groupuntil you have one from each group

Steps for making a simulation5. Run several trials.

repeat several trials – the more the better

Steps for making a simulation6. Analyze the response variable.

List all the response variables from the multiple trials and run the numbers (normal distribution – mean, stddev)

What is the mean and stddev of the What is the mean and stddev of the number of boxes from each trial.number of boxes from each trial.

N( ______ , ______ )

Steps for making a simulation7. State your conclusion in context.

Based on our simulation, we estimate Based on our simulation, we estimate that if you wanted a complete set of the three that if you wanted a complete set of the three pictures you will open an average of _______ pictures you will open an average of _______ boxes of cereal.boxes of cereal.

Go to class practice

You can never trust a candy company!There are 6 flavors of fruit snacks. The company who

makes them says that the packages are randomly filled but that they make 15% of every flavor expect orange and cherry of which they make 20%. You open your package and see that out of 42 candies you have 7 orange snacks.

Did you get cheated out of orange snacks?

The layoffs were sexists!A medium sized firm layed off 10% of its workforce.

They said the layoffs were random and no one group was targeted. Of those who were laid off, 50% were women and 50% were men but the company was made up of 70% men and only 30% women. They obviously targeted women in the layoffs because a greater percentage of women were let go compared to men.

Is there enough evidence to sue the firm?