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AP STATISTICS LESSON 8 - 1

AP STATISTICS LESSON 8 - 1. THE BINOMIAL DISTRIBUTION. ESSENTIAL QUESTION: What is a binomial setting and how can binomial distributions be solved?. Objectives: To identify binomial settings. To become familiar with the binomial formula. To solve problems using the binomial formula.

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AP STATISTICS LESSON 8 - 1

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  1. AP STATISTICSLESSON 8 - 1 THE BINOMIAL DISTRIBUTION

  2. ESSENTIAL QUESTION: What is a binomial setting and how can binomial distributions be solved? Objectives: • To identify binomial settings. • To become familiar with the binomial formula. • To solve problems using the binomial formula.

  3. Introduction In practice, we frequently encounter experimental situations where there are two outcomes of interest. Some examples are: • We use a coin toss to answer a question. • A basketball player shoots a free throw. • A young couple prepares for their first child.

  4. The Binomial Setting • Each observation falls into one of just two categories, which for convenience we call “success” or “failure.” • There is a fixed number n of observations. • The n observations are all independent. (That is, knowing the results of one observation tells you nothing about the other observations). • The probability of success, call it p, is the same for each observation.

  5. Binomial Distribution The distribution of the count X of successes in the binomial settings is the binomial distribution with parameters n and p. The parameter n is the number of observations, and p is the probability of a success on any one observation. The possible values of X are the whole numbers from 0 to n. As an abbreviation, we say that X is B(n,p).

  6. Example 8.1Blood Typespage 440 Blood type is inherited. If both parents carry genes for the O and A blood types, each child has probability of 0.25 of getting two O genes and so of having blood type O. Different children inherit independently of each other. Find n, p and X.

  7. Example 8.2page 440 Deal 10 cards from a shuffled deck and count the number X of red cards. There are 10 observations and each are either a red or a black card. Is this a binomial distribution? If so what are the variables n,p and X?

  8. Example 8.3page 440 An engineer chooses an SRS of 10 switches from a shipment of 10,000 switches Suppose that (unknown to the engineer) 10% of the switches in the shipment are bad. The engineer counts the number X of bad switches in the sample. Is this a binomial situation? Why?

  9. pdf Given a discrete random variable X, the probability distribution function assigns a probability to each value of X. The probability must satisfy the rules for probabilities given in Chapter 6.

  10. Example 8.6page 443 Corinne is a basketball player who makes 75% of her free throws over the course of a season. In a key game, Corinne shoots 12 free throws and makes only 7 of them. The fans think that she failed because she is nervous. Is it unusual for Corinne to perform this poorly?

  11. Example 8.7page 443 We want to determine the probability that all 3 children in a family are girls. Find n, p, and X.

  12. cdf The cumulative binomial probability is useful in a situation of a range of probabilities. Given a random variable X, the cumulative distribution function (cdf) of X calculates the sum of the probabilities for 0,1,2,…, up to the value X. That is , it calculates the probability of obtaining a most X successes in n trials.

  13. Example 8.8page 444 If Corrine shoots n = 12 free throws and makes no more than 7 of them?

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