A. Probability and normal distributions

(f) An online retailer dispatches products from one of three warehouses (A, B and C), where these warehouses account for 10%, 40% and 50% of the retailer's sales, respectively. It is known that the percentage of defective items are 4%, 6% and 3%, from warehouses A, B and C, respectively. A customer complains that they have received a defective item. What is the probability this item came from warehouse A? Provide your answer to four decimal places. (6 marks) (g) A random sample is drawn from a normal distribution, N01, 36). You are told that a 90% condence interval for the population mean is (5.78, 7.22). What was the size of the sample? (5 marks) (h) Explain how you would develop an experimental design to determine the effectiveness of a vaccine