Transcript 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
Be able to recognize when a simulation might usefully model
random behavior in the real-world
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
Be able to describe a simulation so that others could repeat it
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
Random numbers: random numbers are hard to generate.
Nevertheless, several internet sites offer an unlimited supply of
equally random values
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
Trial: the sequence of several components representing events
that we are pretending will take place
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
Explain how you will model the outcome
Explain how you will simulate the trial
Clearly state the response variable
Analyze the response variable
State your conclusion in the context of the problem
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Using the Calculator
To select a random number:
1) Hit MATH
2) Hit PRB menu
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
Don’t overstate your case: a simulation isn’t real, so don’t stretch
the data from the simulation
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?
1) Assign the correct result to numbers 0-7 and incorrect to 7 & 8
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?
1) Assign each couple 1-2, 3-4, 5-6, 7-8… ignore 0,9
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.