| (a) | The cashflows for Project S are given below: | [3] | ||||||||||||
What is the Net Present Value (NPV) for Project S if the cost of capital is 10%?
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| (b) | A manufacturing process produces cylindrical
component parts for the automotive industry. It is important that the process produce
parts having a mean diameter of at least 42.8 millimetres. It is known that the population
variance is s2 = 2.917. A cylinder is chosen at random and found to
have diameter 41.0 millimetres. Calculate the probability that the population mean  is greater than 42.8 millimetres, stating any assumptions that you
make.
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[5] | ||||||||||||
| (c) | Give one example of each of the following types of sets | [1] | ||||||||||||
| (i) A finite set | [1] | |||||||||||||
| (ii) An infinite countable set | [1] | |||||||||||||
| (iii) An infinite uncountable set
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| (d) | Blackburn Rovers, the English professional
football club is looking for a new centre forward. The club can buy one of: Michael Owen
from Liverpool at a cost of £19 million; Andy Cole from Manchester United at a cost of
£9 million; or a promising young player called Tony Grimsey from non-league team
Mansfield Road, at a cost of £1 million. Blackburn believe that they will have a
probability of 0.8 of winning the league if they buy Michael Owen, a probability of 0.4 of
winning the league if they buy Andy Cole, and a probability of 0.1 of winning the league
if they buy Tony Grimsey. Winning the league will increase revenue by £25 million. Which
player should Blackburn buy to maximise their expected revenue.
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[7] | ||||||||||||
| (e) | Give two limitations of simulation techniques. | [2] |