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Introduction to Binomial Distributions

Introduction to Binomial Distributions. Presentation 5.1 Overview and Examples. Binomial Distributions. A binomial distribution or setting is simply the total number of successes in a sequence of n trials. The typical example is the number of heads in a sequence of n coin flips.

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Introduction to Binomial Distributions

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  1. Introduction to Binomial Distributions Presentation 5.1 Overview and Examples

  2. Binomial Distributions • A binomial distribution or setting is simply the total number of successes in a sequence of n trials. • The typical example is the number of heads in a sequence of n coin flips.

  3. Binomial Criteria • In order for a setting to be BINOMIAL, it must fit the following criteria: • Binomial experiment consists of a fixed number, n trials. • Each trial consists of two outcomes: success or failure. • Each trial is independent. • The probability of success p is the same on every trial.

  4. Examples of binomial settings • Number of male, or number of female births in the next 20 births at local hospital. P(male)=.52. • Number of made free throws in next 30 free throws. • Number of correct answers on a 10 question multiple choice exam when guessing. • Number of people that show up for a flight when sold 100 tickets.

  5. Binomial or Not? • Is each of the following binomial or not? The Ford Motor Company chooses one car from each hour’s production for a detailed quality inspection. One variable recorded is the number of blemishes in the paint. NOT There is not a distinct success or failure. There is no limit to the number of blemishes.

  6. Binomial or Not? • Is each of the following binomial or not? The pool for potential jurors for a burglary case contains 70 people chosen at random from the adult residents of Spokane. Each person in the pool is asked if they believe in the “three strikes, your out” law. You record the total number of people who say yes. Binomial There is success or failure (yes or no). Fixed number of trials (70). Independent and constant probability (since randomly selected people).

  7. Binomial or Not? • Is each of the following binomial or not? Joey buys a scratch lottery ticket every week for a year. He records the number of times he wins a prize (any prize). Binomial There is success or failure (prize or no). Fixed number of trials (52). Independent and constant probability (since separate tickets).

  8. Introduction to Binomial Distributions • This concludes this presentation.

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