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Cork Institute of Technology
Bachelor of Science (Honours) in Software Development-
Stage 2
(KSDEV_8_Y2)
Autumn 2008
Mathematics
(Time: 3 hours)
Answer FIVE questions. Examiners: Dr. M. O Cinneide At least ONE question to be attempted Mr. M. Donnelly from each section Dr D. O’Connor Dr S. O Rourke Please use a different answer book for each section.
Section A
Q1. Marketing Ltd has developed a questionnaire for a survey. The following table shows the tasks involved, the immediately preceding tasks, and for each task the most likely estimate, the optimistic estimate and the pessimistic estimate.
Task Preceding tasks
Most likely (m)
Optimistic (a) Pessimistic (b) A Design Questionaire
B Sampling Design - 12 10 20 C Pilot Survey A 5 4 12 D Recruit Interviewers
B 4 2 6
E Train Interviewers
D,A 3 3 3
F Allocate Interviewers
B 4 3 5
G Undertake Interviews
C,E,F 10 8 18
H Data Entry G 3 2 4 I Debrief Interviewers
G 2 2 2
J Data Analysis H 5 4 6 K Write Report I,J 4 2 12
Using the Project Evaluation Review Technique (PERT) the mean time, μ, and the standard deviation, σ, for the duration of each task are estimated from the most likely (m), optimistic (a) and pessimistic (b) estimates by using the formulae: μ = (4m + a + b) / 6 and σ = (b – a) / 6
(a) Draw a network for this questionnaire and use the mean times to find the critical path. (12 Marks) (b) Determine the mean and standard deviation of the critical path duration. (2 Marks)
(c) If the sales manager wants a 0.95 probability of completing the project on time, how far ahead of the scheduled meeting date should he begin working on the project? (3 marks)
(d) What is the probability planning and coordinating the annual training programme will exceed 50 days? (3 Marks)
Q4 Job applications are dealt with in three stages. Two external experts A and B (A and B work in parallel and independently of each other) first review the applications and on receipt of these reports the HR manager make the final decision. The time taken by reviewer A to furnish a report follows the following distribution:
Reviewer A Reporting Time (weeks) 4 5 6 Probability 0.3 0.5 0.
Similarly the time taken by reviewer B is a random variable with probability distribution as follows:
Reviewer B Reporting Time (weeks) 5 6 7 Probability 0.2 0.5 0.
The final stage, undertaken by the directorate, takes place immediately on receipt of these reports (the process begins when both reports have been received). This stage, which ends with the issue of a final decision, takes between two and five weeks with probabilities as follows.
Directorate Decision Making Time (weeks) 2 3 4 5 Probability 0.25 0.35 0.25 0.
(a) Simulate the passage of six applications through the system and from your simulation estimate the average time between receipt of the application by the secretariat and the issue of a decision by the directorate. Show your work clearly.
Random Numbers for Simulation Reviewer A 5, 8, 2, 9, 3, 8 Reviewer B 5, 0, 9, 3, 0, 1 Directorate 38, 47, 52, 35, 41, 92 (10 marks)
(b) What are pseudo random numbers and briefly describe a method for generating a series of these numbers (5 marks)
(c) State four advantages of using simulation techniques (5 marks)
Q5 (a) Five coins are tossed, what is the probability of (i) getting no tails. (ii) three tails (3 marks)
(b) Three cards are drawn at random from a pack. What is the probability of getting of drawing three kings (i) With replacement, (ii) Without replacement. (3 marks)
(c) The lifetime of a certain component is normally distributed with a mean life of 2500 hours and a standard deviation of 800 hours. Find the percentage of components with lives: (i) Between 2100 and 3300 hours. (ii) More than 2700 hours. (iii) The time beyond which the most enduring 5 % of component survive. (6 marks)
(d) In a chemical company production stops on average 3.4 times per month due to machine failure. Assuming a Poisson distribution calculate the probability that in any month (i) There are exactly two stoppages. (ii) There are less than three stoppages. (5 marks)
(e) Twenty percent of a bag of sweets are soft centered and the rest are hard centered. If a handful of five sweets are selected at random, what is the probability that there are exactly 3 soft centered sweets in the handful? (3 marks)
