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KING FAHD UNIVERSITY OF PETROLEUM & MINERALS DEPARTMENT OF MATHEMATICS & STATISTICS DHAHRAN, SAUDI ARABIA STAT 213: Statistical Methods for Actuaries Semester 151 Major Exam Two Thursday, Oct 29, 2015 Allowed time 90 minutes Name: Student ID#: Directions: 4) 1) You must show all your work to obtain full credit. 2) Round probability answers to 4 decimal places. 3) You are allowed to use electronic calculators and other reasonable writing accessories that help in writing the exam. Turn off your mobile with you during the exam. Question No Full Marks Q1 10 Q2 8 Q3 6 Q4 7 Q5 4 Total 35 Marks Obtained Question 1 10 marks Phone calls arrive at the reservation desk for Regional Airways follows Poisson distribution at a rate of 48 per hours. a. Compute the probability of receiving 55 calls in an hour. b. Compute the probability of receiving three calls in a 5 minutes interval of time. c. Compute the probability that the time to next call is more than 3 minutes. Question 2 8 marks The manager of bank wants to reduce the customer waiting time in his branch. He decides to focus on two variables the time spent by the customers in the bank whether customers are satisfied by the banking services or not He selects a random sample of 60 customers during a certain week and found that the mean time spent by these customers was 11.3 minutes, with a standard deviation of 3.1 minutes. i) Construct a 99% confidence interval estimate of the population mean time spent. ii) How many customers need to be selected to have 90% confidence of estimating the population proportion of customers who are satisfied with banking services to be within ±0.04? Question 3 6 marks The mean annual cost of automobile insurance is $939 (CNBC, February 23, 2006). Assume that the standard deviation is $245. a. What is the probability that the cost of automobile insurance is greater than $750? b. 90% of the automobile insurance policies will be contained between what two values symmetrically distributed around the mean? Question 4 7 marks Suppose the random variable X follows uniform distribution for 3.25<x<5.75. i) Find the probability that X lies between 4.5 and 5.90 ii) Suppose a random sample of n = 49 is selected from this population, what is the probability that the sample mean is greater than 4 and less than 5. Question 5 4 marks For a given risk, the number of claims for a single exposure period is given by a binomial distribution with = 0.27 and n = 98. i) Find the probability that the number of claims is exactly 25. ii) Find the approximate probability that the number of claims is 25.