Download stats_8_1_2

Warm Up
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When rolling an unloaded die 10 times, the number
of time you roll a 1 is the count X of successes in
each independent observations.
Is this a Binomial Distribution?
How would you describe this with “B” notation?
I want to know the probability of getting at most 2 of
the 10 rolls will be a success (I roll a 1). Interpret
the binomial probability.
Construct the binomial probability distribution table.
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AP Statistics, Section 8.1.1
Section 8.1.2
Binomial Distributions
AP Statistics
Binomial Distributions
on the calculator
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Binomial Probabilities
B(n,p) with k successes
binompdf(n,p,k)
Corinne makes 75% of
her free throws.
What is the probability of
making exactly 7 of 12
free throws.
binompdf(12,.75,7)=.1032

n k
nk
p
1

p




 
k 
12 
5
7
  .75  .25 
7 
2nd Vars 0:biniompdf
AP Statistics, Section 8.1.2
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Binomial Distributions
on the calculator
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12 
12 
5
7
6
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Binomial Probabilities
.75
.25

.75
.25
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

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 
 
7 
6 
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B(n,p) with k successes
12 
12 
5
7
binomcdf(n,p,k)
   .75 .25     .754 .258 
5 
4 
Corinne makes 75% of
12 
12 
her free throws.
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   .75 .25     .752 .2510 
What is the probability of  3 
2 
making at most 7 of 12
12 
12 
1
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   .75 .25     .750 .2512 
free throws.
1 
0 
binomcdf(12,.75,7)=.1576
AP Statistics, Section 8.1.2
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Binomial Distributions
on the calculator
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Binomial Probabilities
B(n,p) with k successes
binomcdf(n,p,k)
Corinne makes 75% of
her free throws.
What is the probability of
making at least 7 of 12
free throws.
1-binomcdf(12,.75,6)=
12 
12 
5
7
8
4
.75
.25

.75
.25

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
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

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 
 
7 
8 
12 
12 
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   .75 .25     .7510 .252 
9 
10 
12 
 12 
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1
   .75 .25     .7512 .250 
11 
 12 
AP Statistics, Section 8.1.2
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Binomial Simulations
Corinne makes 75% of her free throws.
 Simulate shooting 12 free throws.
 randBin(n,p) will do one simulation
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MATHPRB 7:randBin
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randBin(n,p,t) will do t simulations
AP Statistics, Section 8.1.2
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Normal Approximation of
Binomial Distribution
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Remember
  np
  np 1  p 
AP Statistics, Section 8.1.2
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Normal Approximation of
Binomial Distribution
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As the number of trials n gets larger, the
binomial distribution gets close to a normal
distribution.
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“The accuracy of the normal approximation improves
as the sample size n increases. It is most accurate for
any fixed n when p is close to ½ and least accurate
when p is near 1 or 0.” Pg.454
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Question: What value of n is big enough, so
let’s see how the close two calculations are…
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Example:
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A recent survey asked a nationwide
random sample of 2500 adults if they
agreed or disagreed that “I like buying new
clothes, but shopping is often frustrating
and time-consuming.” Suppose that in fact
60% of all adults would “agree”. What is
the probability that 1520 or more of the
sample “agree”.
AP Statistics, Section 8.1.2
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TI-83 calculator
B(2500,.6) and P(X>1520)
 1-binomcdf(2500,.6,1519)
 .2131390887
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AP Statistics, Section 8.1.2
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Exercises
AP Statistics, Section 8.1.2
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