Section 8.1.2
Binomial Distributions
AP Statistics
www.toddfadoir.com/apstats
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 
AP Statistics, Section 8.1.2
2
Binomial Distributions
on the calculator
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12 
12 
5
7
6
6
Binomial Probabilities
.75
.25

.75
.25







 
 
7 
6 


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.
3
9
   .75 .25     .752 .2510 
What is the probability of  3 
2 
making at most 7 of 12
12 
12 
1
11
   .75 .25     .750 .2512 
free throws.
1 
0 
binomcdf(12,.75,7)=.1576
AP Statistics, Section 8.1.2
3
Binomial Distributions
on the calculator






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







 
 
7 
8 
12 
12 
9
3
   .75 .25     .7510 .252 
9 
10 
12 
12 
11
1
   .75 .25     .7512 .250 
11 
12 
AP Statistics, Section 8.1.2
4
Binomial Simulations
Corinne makes 75% of her free throws.
 Simulate shooting 12 free throws.
 randBin(n,p) will do one simulation
 randBin(n,p,t) will do t simulations
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AP Statistics, Section 8.1.2
5
Normal Approximation of
Binomial Distribution
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Remember
  np
  np 1  p 
AP Statistics, Section 8.1.2
6
Normal Approximation of
Binomial Distribution
As the number of trials n gets larger, the
binomial distribution gets close to a normal
distribution.
 Question: What value of n is big enough?
The book does not say, so let’s see how
the close two calculations are…
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AP Statistics, Section 8.1.2
7
Example:

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
8
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
9
Exercises

8.8-8.11 all, 8.15-8.19 odd, 8.27-8.35 odd
AP Statistics, Section 8.1.2
10