A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 50 ml of coffee. The machine actually dispenses a mean amount of 55 ml per cup and 10% of the cups contain less than the amount stated on the sign. Assuming that the amount of coffee dispensed into each cup is normally distributed, what percentage of cups contain more than 61 ml of coffee? Following complaints, the owners of the machine make adjustments. Only 2.5% of the cups now contain less than 50 ml. The standard deviation of the amount dispensed is now reduced to 3 ml. Assuming that the amount of coffee dispensed is still normally distributed, find the new mean amount of coffee per cup.

b. A computer repair shop gets computers on regular basis for repairs. The repair time between two computers is exponentially distributed with mean time between repairs of two computers being 2 hours. Find the conditional probability that a repair of a computer takes at least 10 hours given that duration of the repair exceeds 9 hours. Re-compute the answer if distribution of repair time is assumed to be uniformly distributed between 0 and 20 hours.