A cola-dispensing machine is set to dispense the mean of 2.02 liters in a bottle labeled 2 liters. Actual quantities dispensed vary as well as the amounts are normally distributed with the standard deviation of 0.015 liters. Do all of the following by hand - show work.
a. Determine the probability a bottle will have between 2.02 and 2.04 liters?
b. What is the probability a bottle will contain between 2.00 and 2.03 liters?
c. What is the probability a bottle will contain less than 2 liters?
d. How much cola is dispensed in the largest 4% of the drinks?