Stats 309 7-4

# Stats 309 7-4 - 7.4 Binomial Distribution The binomial...

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7.4 Binomial Distribution The binomial distribution is the result of a binomial experiment. Only two possible outcomes For example: coin flip, product is defective or not, male or female – Usually labeled as Success or Failure – Whatever you are ‘looking for’ is labeled a Success. – Usually define a random variable to count how many Successes. Binomial Experiment Consists of a fixed number of n trials. – Result of each trial can be classified as S or F (two possible outcomes). – The probability, p, of a success remains constant for each trial. – Each trial is independent of the other trials.

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Examples Flip a coin 10 times. Two outcomes per trial. If we are betting on heads, we would label heads a success. If the coin is fair, the probability of heads is 50%, so p = .5. Trials are independent since the outcome of one flip does not affect the outcome of other flips. n = 10 p = .5 q = 1 – p = .5 Draw 5 cards out of a shuffled deck. We can label as success whatever card we seek, say clubs. Two outcomes are clubs or not. The probability of getting a club on the first draw is 13/52. We have to replace the card for the second draw or we won’t have independence. Why? n = 5 p = 13/52 q = 39/52
Example A factory makes computer chips. We decide to test 500 randomly selected chips to determine whether defective or not. The defective rate at this factory is 1%.

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Stats 309 7-4 - 7.4 Binomial Distribution The binomial...

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