Cork Institute of Technology
Bachelor of Science (Honours) in Advanced Manufacturing Technology
Bachelor of Science (Honours) in Process Plant Technology
January 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, 20, 30 and 50 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 defective?
(ii) If it is found to be defective, what is the probability that it was produced by machine A?
(8 marks)
(b) P(A) = 0.4, P(B)=0.5 and P(A or B) = 0.7.
Show that A and B are 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. Two wafers are to be randomly selected for inspection. Find the probability that
(i) both are non-defective
(ii) one of the two is non-defective (6 marks)
2. (a) The probability that an electronic timer is non-conforming is 0.03. A sample of size 50 is
taken from a large batch of such items. Determine the probability of finding 2 or fewer
non-conforming timers
(i) using the Binomial distribution
(ii) using the Poisson approximation. (8 marks)
