The amount of regular unleaded gasoline purchased every week at a gas station near UCLA follows the normal distribution with mean 50,000 gallons and standard deviation 10,000 gallons. The starting supply of gasoline is 74,000 gallons, and there is a scheduled weekly delivery of 47,000 gallons. a. Find the probability that, after 11 weeks, the supply of gasoline wil be below 20,000 gallions.
b. How much should the weekly delivery be so that after 11 weeks the probability that the supply is below 20,000 gallons is only 0.5%?