4.2 Binomial Distributions

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Presentation transcript:

4.2 Binomial Distributions Important Concepts Binomial Experiment Binomial Probability Formula Mean (or Expected Value), Variance, and Standard Deviation of a Binomial Random Variable

4.2 Binomial Distributions So what exactly is a Binomial Experiment? A probability experiment that satisfies the following four conditions: The experiment is repeated for a fixed number of trials, where each trial is independent of the other trials. There are only two possible outcomes of interest for each trial (either a success, S, or a failure, F). The probability of a success is the same for each trial. The random variable X counts the number of successful trials.

4.2 Binomial Distributions #16 p. 211 (Childhood Obesity) We’ll start with 3 U.S. adults instead of 6. Binomial Probability Formula valid for x = 0,1,2,…,n #16 p. 211 Let’s work with all 6 adults this time.

4.2 Binomial Distributions Mean, Variance, and Standard Deviation of a Binomial Random Variable: Good news! We do not have to build tables like we did in the last section to find these parameters. We can use formulas!

4.2 Binomial Distributions #29 p. 212 (Life on Mars) We could also construct a probability histogram for this binomial random variable. Since p < 0.50, we would expect the graph to be skewed to the right.