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Susan is a sales representative who has a history of making a successful sale from about 74 of her sales contacts If she makes 12 successful sales this week Susan will get a bonus Let n be a andom variable representing the number of contacts needed for Susan to get the 12th sale a Explain why a negative binomial distribution is appropriate for the random variable n We have binomial trials for which the probability of success is p 0 74 and failure is q 0 26 k is a fixed whole number 2 1 We have binomial trials for which the probability of success is p 0 26 and failure is q 0 74 k is a fixed whole number 2 1 We have poisson trials for which the probability of success is p 0 74 and failure is q 0 26 k is a fixed whole number 1 O We have binomial trials for which the probability of success is p 0 74 and failure is q 0 26 k is a fixed whole number 1 Write out the formula for P n in the context of this application Use C a b as the notation for a choose b P n 1 X b Compute P n 12 P n 13 and P n 14 Use 4 decimal places P 12 0 0270 P 13 0 0842 P 14 0 1424 X x c What is the probability that Susan will need from 12 to 14 contacts to get the bonus Use 4 decimal places 0 2536 x d What is the probability that Susan will need more than 14 contacts to get the bonus Use 4 decimal places 0 7464 X e What are the expected value and standard deviation a of the random variable n Use 2 decimal places 3 87 x 2 39 Interpret these values in the context of this application O The expected contact in which the thirteenth sale occurs is with a standard deviation of a O The expected contact in which the twelfth sale occurs is o with a standard deviation of O The expected contact in which the eleventh sale occurs is with a standard deviation of a The expected contact in which the twelfth sale occurs is with a standard deviation of a

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