ENGG201 School of Engineering 45367 Examiner: Dr A Haworth Question 3 [25 marks] An engineer works in a research lab and wants to build a device to measure pressure. As a

result, they are looking for a company to supply plastic tubing. (a) Company A supplies tubing. However, on average it has 4 pin holes per 5 m of tubing. (0) If the engineer selects a 5 m length of tubing, what is the probability it will contain less than 3 pin holes? (1) (ii) If the engineer selects 1 m of tubing, what is the probability it will contain no pin holes? [8 marks] (b) The engineer has picked two companies which provide the lab with precut 1 m lengths of plastic tubing. Company B supplies 70 % of all the tubing in the lab, whilst Company C supplies the rest. The probability that there is a pin hole in a length of tube is 2 % and 5% for Company B and Company C, respectively. The engineer picks up a random piece of tubing in the lab and notices that it has a pin hole. What is the probability that it was supplied by Company B? What is the probability that a randomly chosen piece of tubing has a pin hole? [6 marks] (c) The engineer wants to build a manometer out of the plastic tubing. With the aid of diagrams, explain how an inclined manometer works and why it might be used instead of a u-shaped manometer. [6 marks] (d) The lab decides to buy a pack of 25 capacitive pressure transducers. On the manufacturer's website it states that the probability of one of its sensors being defective is 0.05. Determine the probability of 3 of the sensors being defective in the pack of 25. [5 marks]