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.

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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

Section Binomial Distributions AP Statistics

AP Statistics, Section 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

AP Statistics, Section 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

AP Statistics, Section 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)=

AP Statistics, Section 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

AP Statistics, Section Normal Approximation of Binomial Distribution Remember

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…

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

AP Statistics, Section Exercises