Section 8.1.2 Binomial Distributions

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# Section 8.1.2 Binomial Distributions - PowerPoint PPT Presentation

Section 8.1.2 Binomial Distributions. AP Statistics www.toddfadoir.com/apstats. Binomial Distributions on 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.

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### Section 8.1.2Binomial Distributions

AP Statistics

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

AP Statistics, Section 8.1.2

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

AP Statistics, Section 8.1.2

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)=

AP Statistics, Section 8.1.2

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

Normal Approximation of Binomial Distribution
• Remember

AP Statistics, Section 8.1.2

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

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

TI-83 calculator
• B(2500,.6) and P(X>1520)
• 1-binomcdf(2500,.6,1519)
• .2131390887

AP Statistics, Section 8.1.2

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

AP Statistics, Section 8.1.2