### Chp 11

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AP Statistics: Chapter 11
Pages 258-269
Rohan Parikh
Azhar Kassam
Period 2
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Goals

Be able to recognize random outcomes in a real-world situation
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Be able to recognize when a simulation might usefully model
random behavior in the real-world
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Know how to perform a simulation either by generating random
numbers on a computer or calculator, or by using some other
source of random values, such as dice, a spinner, or a table of
random values
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Be able to describe a simulation so that others could repeat it
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Be able to discuss the results of a simulation study and draw
conclusions about the questions being investigated
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Terms

Random: an event is random if we know what outcomes could
happen, but not which particular values will happen
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Random numbers: random numbers are hard to generate.
Nevertheless, several internet sites offer an unlimited supply of
equally random values
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Simulation: a simulation models random events by using random
numbers to specify event outcomes with relative frequencies that
correspond to the true real-world relative frequencies we are
trying to model.

Simulation component: the most basic situation in a simulation iin
which something happens at random
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Terms

Outcome: an individual result of a component of a simulation is
considered the outcome
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Trial: the sequence of several components representing events
that we are pretending will take place
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Response variable: values of the response variable record the
results of each trial with respect to what we are interested in
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Steps in Conducting a Simulation

Identify the component to be repeated
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Explain how you will model the outcome
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Explain how you will simulate the trial
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Clearly state the response variable
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Analyze the response variable
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State your conclusion in the context of the problem
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Using the Calculator
 To select a random number:
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

1) Hit MATH
3) Hit 5:randInt(
 randInt(0,1): selects a random number between 0 and 1
 randInt(1,6): selects a random number between 1 and 6, which
is similar to rolling a dice
 randInt(1,6,2): selects two random numbers between 1 and
six, very similar to rolling two dice
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Example

A cereal box manufacturer advertises that they put a picture of a
famous athlete in each box. Tiger Woods accounts for 20%, Lance
Armstrong for 30%, and the rest Serena Williams. How many boxes
of cereal does one have to buy in order to get all three pictures.
 Step 1: Assign numbers, 0-9, to each athlete based on
percentage.
 TW: 0,1; LA: 2,3,4; SW: 5,6,7,8,9
 Step 2: Set up a random simulation and begin picking numbers
between 1-10 continuously until all three groups are picked
 Step 3: Run multiple trials and average the number of boxes the
trial takes.
 EX: 137 2554251 1123428 82320 4553241
 On average, it takes 5.8 ((3+7+7+5+7)/5) boxes to obtain all 3
pictures.
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Things to Remember
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Don’t overstate your case: a simulation isn’t real, so don’t stretch
the data from the simulation
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Model the outcome chances accurately: Do not overlook key
points from the data or situation

Run enough trials: makes the data accurate and useable
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Homework Problem #13

You take a quiz with 6 MC questions. After studying, you assume
you have an 80% chance to get an individual question correct.
What are the chances of getting all the questions right?
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1) Assign the correct result to numbers 0-7 and incorrect to 7 & 8
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2) Run 20 trials, picking 6 numbers randomly each time.


If all 6 are between 0-7, all would be correct. Otherwise, you got a
question wrong.
3) 915467 392782 320105 892310 704390 862973 289016 963091
312835 60067 831496 569675 326814 428944 266874 963488
274420 361605 209827 217258
 All correct occurs 5 out of 20 times… 25% chance to get all right
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Homework Problem #31

4 couples at a party decide to play a game. If each of the 8 people
write their name on a slip, what is the chance that every person will be
paired with someone other than who they came with?
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1) Assign each couple 1-2, 3-4, 5-6, 7-8… ignore 0,9
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2) Randomly select 4 groups of two numbers as a trials… run 11 trials

3) [8,4 1,4 6,3 6,7] [3,2 7,4 3,6 8,6] [2,4 3,2 3,8 2,5] [3,6 7,3 4,5 4,8]
[2,4 2,8 4,1 3,8] [4,5 1,2 2,8 2,5] [3,5 3,6 4,6 2,5] [2,7 4,5 2,4 3,4]
[1,5 1,2 2,4 5,8] [3,7 1,6 3,7 1,2] [1,8 1,5 1,7 6,8]

This simulation shows that each person does not pair up with a
new person 4/11 times, so 7/11 times of the time results in each
person paired up with a new person. This equates to 36.4% of the
time.
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