Tanker trucks are designed to carry huge quantities of gasoline from refineries to filling stations. A factory that manufactures the tank of the trucks claims to manufacture tanks with a capacity of 8550 gallons of gasoline. The actual capacity of the tanks is normally distributed with mean µ=8544 gallons and standard deviation σ=12 gallons.

a. Find the z-score corresponding to a tank with a capacity of 8550 gallons. Round your answer to three decimal places.
b. What is the probability that a randomly selected tank will have a capacity of less than 8550 gallons?
c. A simple random sample of n = 50 tanks will be selected. What is the probability that the mean capacity for these 50 tanks will be greater than 8540 gallons?
d. A simple random sample of n = 20 tanks will be selected. Find the z-score corresponding to a sample mean capacity for 20 tanks of 8550. Round your answer to three decimal places. =?