4. (9 pts) Twenty percent of wells drilled in areas deemed favorable strike oil. A company has 50 wells at different sites. Define S as the number of wells that strike oil out of the 50 sites , and let Q be the proportion of wells owned by the company that strike oil, that is, Q = 5/50. 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). c. Calculate the variance of Q. Save result to 4 decimal points . 5. (12 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 a. Can the above problem be formulated as a binomial experiment? Why? b. What kind of probability distribution does the above satisfy, and is there a function for solving such problems? c. What is the probability that both customers received damaged VCRs? d. What is the probability that one of the two customers received a damaged VCR? 6. (18 pts) An insurance company has determined that each week an average of nine claims are filed in their Atlanta branch .Assume the probability of receiving a claim is the same and independent for any time intervals .What is the probability that during the next week a. exactly seven claims will be filed? b. no claims will be filed? c. at least three claims will be filed '? d. What is the probability that during the next 2 weeks the company will receive less than 4 claims? 7. (7 pts) The scheduled time of arrival of a flight to New York is 8:00 a.m. However, the actual time of arrival is (8 + X) a.m., where X is a random variable having the following probability density function: {(c3+1)? '2', ?>0, ?(9) = O, o?h???i??. a. Find the value of the constant c in the probability density function . b. What is the probability that the flight will arrive between 9:00 a.m. to 10:00 a.m.? Save result to 3 decimal points