6. (11 points} Let X represent the amount of gasoline (gallons) purchased by a randomly selected customer at a gas station. Suppose that the mean and standard deviation of X are 11 gallons and 5 gallons, respectively. {a} In a sample of 513 randomly selected customers, what is the approximate probability that the sample mean of the amount purchased J? is at least 12 gallons? [Hint use the central iimir theorem] {b} In a sample of 513 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at least gallons