Q2. Metal tubes fitment

This question may be handwritten and then scanned to pdf, or typed up. A manufacturer makes metal tubes which must t into metal sleeves. The metal tubes have an average diameter of ,umm with a standard deviation of 0.5mm. The sleeves have an average interior diameter of (,u + 1)mm with a standard deviation of 0.4cm. Both diameters are assumed to be normally distributed. (a) What is the probability that a randomly selected tube will t into a randomly selected sleeve? '4 marks] (b) Given that the tube ts, what is the probability that the difference in diameters will be less than 1.5mm? 3 marks] (c) What is the probability that the average diameter of 10 randomly selected tubes will be less than ,u + 0.5mm? '4 marks] ((1) How many tube samples do we need to collect if we would like our sample mean to be within 0.1mm of p, with probability 0.95? '4 marks]