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Lecture_09,_Chap_6,_Sec_2

# Lecture_09,_Chap_6,_Sec_2 - Chapter 6 Section 2 The...

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Sullivan – Statistics : Informed Decisions Using Data – 2 nd Edition – Chapter 6 Section 2 – Slide 1 of 32 Chapter 6 Section 2 The Binomial Probability Distribution

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Binomial Distribution Learning objectives Determine whether a probability experiment is a binomial experiment Compute probabilities of binomial experiments Compute the mean and standard deviation of a binomial random variable Construct binomial probability histograms 1 2 3 4
Binomial Distribution A binomial experiment has the following structure The first test is performed … the result is either a success or a failure The second test is performed … the result is either a success or a failure. This result is independent of the first and the chance of success is the same A third test is performed … the result is either a success or a failure. The result is independent of the first two and the chance of success is the same

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Binomial Distribution Example: A card is drawn from a deck. A “success” is for that card to be a heart … a “failure” is for any other suit The card is then put back into the deck A second card is drawn from the deck with the same definition of success. The second card is put back into the deck We continue for 10 cards
Binomial Distribution A binomial experiment is an experiment with the following characteristics The experiment is performed a fixed number of times, each time called a trial The trials are independent Each trial has only two possible outcomes, usually called a success and a failure The probability of success is the same for every trial

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Binomial Distribution Notation used for binomial distributions The number of trials is represented by n The probability of a success is represented by p The total number of successes in n trials is represented by X Because there cannot be a negative number of successes, and because there cannot be more than n successes (out of n attempts) 0 ≤ X n
Binomial Distribution In our card drawing example: Each trial is the experiment of drawing one card The experiment is performed 10 times, so n = 10 The trials are independent because the drawn card is put back into the deck Each trial has two possible outcomes, a “success” of drawing a heart and a “failure” of drawing anything else The probability of success is 0.25, the same for every trial, so p = 0.25 X , the number of successes, is between 0 and 10

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Binomial Distribution The word “success” does not mean that this is a good outcome or that we want this to be the outcome
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