1. The amount of regular unleaded petrol purchased every week at a gas station near the University of Queensland follows the normal distribution with mean 50000 litres and standard deviation 10000

litres. There is a scheduled delivery of 47000 litres at the beginning of each week. Immediately after the delivery at the beginning of Week 1, the supply of petrol was 121 000 litres. (a) Find the probability that, at the end of Week 11, the supply of petrol will be below 20000 litres. [7 marks] (b) How large should the weekly delivery be so that, at the end of Week 11, the that the supply is below 20000 litres is only 0.5%? probability [8 marks]