1. Section 6.3 Second Day Binomial Calculations on the TI µ and σ of a Binomial RV

2. Is this a binomial setting? Deal 10 cards from a well-shuffled deck of cards. Let X = the number of red cards. Is this a binomial distribution? If so, what are n and p ? If so, what are n and p ? If not, why not? If not, why not?

3. Using the Calculator to Find Binomial Probabilities Under 2 nd DISTR, find 0:binompdf( This command finds probabilities for the binomial probability distribution function. The parameters for this command are n, p, k IN THAT ORDER.

4. Example Let’s go back to the couple having five children. Let X = # of children with type O blood. p = P(success) = P(O blood) = 0.25 The possible values for X are what? Using the binompdf(n,p,k) command, what is the probability that the couple will have 1 child with O blood?

5. Cumulative Distribution Function The pdf command lets you find probabilities for ONE value of X at a time. The cdf command finds cumulative probabilities. We can use it to quickly find probabilities such as P(X < 7) or P(X ≥ 4). The cdf will give you X ≤ Think of this like Table A Think of this like Table A

6. Using the Calculator P(X=k)Binompdf(n,p,k) P(X<k)Binomcdf(n,p,k-1) P(X≤k)Binomcdf(n,p,k) P(X>k)1-Binomcdf(n,p,k) P(X≥k)1-Binomcdf(n,p,k-1)

7. Batch’s Free Throws Chris makes 75% of his free throws over the course of a season. In a key game, he shoots 12 free throws and makes 7 of them. Is it unusual for him to shoot this poorly? What is the probability that Chris makes at least 6 of the 12 free throws? How many free throws would we expect Chris to make?

8. The Mean and Standard Deviation of a Binomial Random Variable The mean of a binomial random variable is np. This formula, while intuitive, is given to you on the AP Exam. This formula, while intuitive, is given to you on the AP Exam. The standard deviation of a binomial random variable is This formula is also given to you. What is the standard deviation for the number of free throws Chris is expected to make?

9. The Mean and Standard Deviation of a Binomial Random Variable Expected value of X is the same as _____________ of X. Let’s go back to the couple having five children. Let X = # of children with type O blood. p = P(success) = P(O blood) = 0.25 What is the expected number of children with type O blood? What is the standard deviation?

10. How the AP folks force you to use the formula In a carnival game, a person can win a prize by guessing which one of 5 identical boxes contains the prize. If a person makes 4 guesses, what is the probability that the person wins a prize exactly 2 times?

11. And yet another way… What is the mean of the random variable X if