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5. (10 pts) A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment .The retailer

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5. (10 pts) A retailer of electronic equipment received six VCRs from the manufacturer. Three of the VCRs were damaged in the shipment .The retailer sold two VCRs to two customers .We are interested in the number of damaged VCRs sold to the customers. Don't use Excel function for the following questions. a. Can a binomial formula be used for the solution ofthe above problem? b. What kind of probability distribution does the above satisfy , and is there a tnction for solving such problems? c. What is the probability that both customers received damaged VCRs 'F d. What is the probability that one of the two customers received a damaged VCR '? 6. (9 pts) Twenty percent of wells drilled in areas deemed favorable strike oil. A company has 30 wells at different sites . Dene S as the number of wells that strike oil out of the 30 sites , and let Q be the proportion of wells owned by the company that strike oil, that is, Q = 5/30. a. What is the distribution of S? State clearly the parameter values associated with the distribution b. Calculate the expected proportion of wells that strike oil, E(Q}. 0. Calculate the variance of Q. Save result to 4 decimal points . 7. (7 pts) The scheduled time of arrival of a ight to New York is 8:00 a.m . However , the actual time of arrival is (8 + X), where X is a random variable having the following probability density function: (assume there is no upper bound for the arrival time) 2mm- x>0, c = El f(x) 0, otherwise. a. Find the value of the constant c in the probability density mction . b. What is the probability that the ight will arrive between 9:00 a.m . to 10 :00 a.m .? Save result to 3 decimal points . 8. (16 pts) The average starting salary for this year's graduates at a large university (LU) is $20,000 with a standard deviation of $8,000 . Furthermore , it is known that the starting salaries are normally distributed Write down both theoretical probability functions and Excel functions for all the sub questions below

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