Cork Institute of Technology
Bachelor of Science (Honours) in Advanced Manufacturing Technology
Bachelor of Science (Honours) in Process Plant Technology
Summer 2005
Bridging Mathematics
(Time: 1.5 hours)
Answer three questions.
All questions carry equal marks.
Statistical tables are provided.
Examiners: Mr. D O’Hare
1. (a) In a factory, machines A, B and C produce, respectively, 50, 20 and 30 percent of
the total output. Of their respective outputs 5, 3 and 2 percent are defective. An
item is chosen at random.
(i) What is the probability that it is not defective?
(ii) If it is found not to be defective, what is the probability that it was produced by
machine C? (8 marks)
(b) P(A) = 0.4, P(B)=0.5 and P(A or B) = 0.8.
Show that A and B are not independent. (6 marks)
(c) An incoming lot of silicon wafers is to be inspected for defectives by an engineer in
a microchip manufacturing plant. In a tray containing twenty wafers, assume that
four are defective. Three wafers are to be randomly selected for inspection. Find
the probability that
(i) all three are non-defective;
(ii) at least one of the three is non-defective. (6 marks)
2. (a) The probability that an electronic timer is non-conforming is 0.02. A sample of
size 1000 is taken from a large batch of such items. Determine the probability of
finding more than non-conforming timers
(i) using the Binomial distribution;
(ii) using the Poisson approximation. (8 marks)
