4.2 binomial distributions important concepts –binomial experiment –binomial probability formula...
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4.2 Binomial Distributions
• Important Concepts– Binomial Experiment– Binomial Probability Formula– Mean (or Expected Value), Variance, and
Standard Deviation of a Binomial Random Variable
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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.
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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.
( ) x n xP X x nCx p q
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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!
2
np
npq
npq
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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.