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Section 8.1.2 Binomial Distributions

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 8.1.2 Binomial Distributions

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

  2. 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

  3. 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

  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 least 7 of 12 free throws. • 1-binomcdf(12,.75,6)= AP Statistics, Section 8.1.2

  5. 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

  6. Normal Approximation of Binomial Distribution • Remember AP Statistics, Section 8.1.2

  7. 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

  8. 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

  9. TI-83 calculator • B(2500,.6) and P(X>1520) • 1-binomcdf(2500,.6,1519) • .2131390887 AP Statistics, Section 8.1.2

  10. Exercises • 8.8-8.11 all, 8.15-8.19 odd, 8.27-8.35 odd AP Statistics, Section 8.1.2

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