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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.