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 50 randomly selected customers, what is the approximate probability that the sample mean of the amount purchased is at least 12 gallons? [Hint: use the central limit theorem]

(b) In a sample of 50 randomly selected customers, what is the approximate probability that the total amount of gasoline purchased is at least 600 gallons?