Expensive and Hence - Bridging Mathematicsy- Exam, Exams of Mathematics

Download Expensive and Hence - Bridging Mathematicsy- Exam and more Exams Mathematics in PDF only on Docsity! Cork Institute of Technology Bachelor of Science in Advanced Manufacturing Technology Bachelor of Science in Process Plant Technology January 2006 Bridging Mathematics (Time: 1.5 hours) Answer three questions. All questions carry equal marks. Statistical tables are provided. Examiner: Mr. D O’Hare 1. (a) Two methods, A and B, are available for teaching a certain industrial skill. The failure rate is 10% for A and 5% for B. However, B is more expensive and hence is used only 40% of the time, with A being used the other 60%. (i) What proportion of workers learn the skill properly? (ii) A worker learns the skill properly. What is the probability that he was taught by method B? (8 marks) (b) P(A) = 0.4, P(B)=0.5 and P(A or B) = 0.8. Are A and B (i) independent? (ii) mutually exclusive? Justify your answer in each case. (5 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-five wafers, assume that five are defective. Three wafers are to be randomly selected for inspection. Find the probability that (i) all three are non-defective; (ii) at least two of the three are non-defective. (7 marks) 2. (a) A company purchases large lots of a certain type of electronic device. A method is used that rejects a lot if 2 or more defectives are found in a random sample of 50 units. (i) What is the probability of accepting a lot that is 2% defective? (ii) What is the probability of rejecting a lot that is 4% defective? (7 marks) (b) Because of faults in an apparatus to supply a gas, the apparatus requires attention on average 1.6 times a day. (i) What is the probability that the apparatus will require no attention during any given day? (ii) In a working week of 5 days, what is the probability that the apparatus will require attention on more than 10 occasions? (7 marks) (c) Specifications require that a product have certain quality characteristics, which can only be determined by a destructive test. The current inspection scheme is to select an initial sample of five items from each batch. If all five meet the quality specification, we accept the batch. If two or more fail, we reject the batch. If one fails, we take a further sample of two items. If both pass the inspection, we accept the batch, otherwise we reject. What is the probability that (i) a batch that is 3% defective is accepted on the basis of the first sample? (ii) a batch that is 3% defective is accepted? (6 marks) 3. (a) Inside diameters of steel pipes produced by a certain firm are N(10,0.1), measured in inches. Pipes with diameters outside the range 10.05 ± 0.12 are considered as defective. (i)Verify that the probability of a defective item is 0.2866 (ii) If the process is adjusted so that the inside diameters will be distributed as N(10.10, 0.1) ,what will be the probability of a defective? (8 marks) (b) Resistors of a certain type have resistances that average 200 ohms with a standard deviation of 10 ohms. Twenty five of these resistors are to be used in a circuit. Find the probability that the mean resistance of the 25 resistors is between 199 and 202 ohms. (6 marks)