Section 8.1.2Binomial Distributions

AP StatisticsJanuary 12, 2009CASA

AP Statistics, Section 8.1.2 2

AP Statistics, Section 8.1.2 3

Binomial Distributionson the calculator 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

1n kkn

p pk

5712.75 .25

7

AP Statistics, Section 8.1.2 4

Binomial Distributionson 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 most 7 of 12 free throws.

binomcdf(12,.75,7)=.1576

57 6 6

5 7 4 8

3 9 2 10

1 11 0 12

12 12.75 .25 .75 .25

7 6

12 12.75 .25 .75 .25

5 4

12 12.75 .25 .75 .25

3 2

12 12.75 .25 .75 .25

1 0

AP Statistics, Section 8.1.2 5

Binomial Distributionson 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)=

57 8 4

9 3 10 2

11 1 12 0

12 12.75 .25 .75 .25

7 8

12 12.75 .25 .75 .25

9 10

12 12.75 .25 .75 .25

11 12

AP Statistics, Section 8.1.2 6

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

AP Statistics, Section 8.1.2 7

Normal Approximation of Binomial Distribution Remember

1

np

np p

AP Statistics, Section 8.1.2 8

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…

AP Statistics, Section 8.1.2 9

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 10

TI-83 calculator

B(2500,.6) and P(X>1520) 1-binomcdf(2500,.6,1519) .2131390887

AP Statistics, Section 8.1.2 11

Exercises

8.8-8.11 all, 8.15-8.19 odd, 8.27-8.35 odd