Q1. (CLO K2) (6 marks)
a) Assume that the length of life of electric bulbs Is normally distributed with
mean 2000 h and standard deviation 250 h, the measurements being
taken to the nearest hour. Find the probability that a given bulb will have a
life between 1800 h and 2015 h. (2 marks)
b) The time between telephone calls to a cable television service call center
follows an exponential distribution with a mean of 1.5 minutes.
What is the probability that the time between the next two calls will be 45
seconds or less? (2 marks)
c) It is known that 5 per cent of a very large number of screws are oversize.
What is the probability that in a sample of 20 screws there will be less than
two oversize? (2 marks)
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Q2. (CLO S2) (4 marks)
A financial advisor has recommended two possible mutual funds for investment:
Fund A and Fund B. The return that will be achieved by each of these depends
on whether the economy is good, fair, or poor. A payoff table has been
constructed to illustrate this situation:
Investment
Fund A
Fund B
Probability
State of Nature
Good Economy
Fair Economy
$12,000
$4,000
$8,000
$5,000
0.2
0.3
Poor Economy
− $6,000
0
0.5
a) What decision model should be used? (1 mark)
b) Perform the necessary calculations to determine which of the two mutual
funds is better. Which one should you choose to maximize the expected
value? (2 marks)
c) Suppose there is a question about the return of Fund A in a good
economy. It could be higher or lower than $12,000. What value for this
would cause a person to be indifferent between Fund A and Fund B (i.e.,
the EMVs would be the same)? (1 mark)
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