1. Warm Up 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. 1. Is this a Binomial Distribution? 2. How would you describe this with “B” notation? 3. 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. 4. Construct the binomial probability distribution table. AP Statistics, Section 8.1.1 1

2. Section 8.1.2 Binomial Distributions AP Statistics

3. AP Statistics, Section 8.1.2 3 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. binompdf(12,.75,7)=.1032  2 nd Vars  0:biniompdf

4. AP Statistics, Section 8.1.2 4 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 most 7 of 12 free throws. binomcdf(12,.75,7)=.1576

5. AP Statistics, Section 8.1.2 5 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)=

6. 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 MATH  PRB  7:randBin randBin(n,p,t) will do t simulations

7. AP Statistics, Section 8.1.2 7 Normal Approximation of Binomial Distribution Remember

8. 8 Normal Approximation of Binomial Distribution As the number of trials n gets larger, the binomial distribution gets close to a normal distribution. “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 Question: What value of n is big enough, so let’s see how the close two calculations are…

9. 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”.

10. AP Statistics, Section 8.1.2 10 TI-83 calculator B(2500,.6) and P(X>1520) 1-binomcdf(2500,.6,1519).2131390887

11. AP Statistics, Section 8.1.2 11 Exercises