The volume of the milk produced in a single milking session by a certain breed of cow is Normally distributed with mean 2.3 gallons with a standard deviation of 0.96 gallons.

Part A Calculate the probability that a randomly selected cow produces between 2.0 gallons and 2.5 gallons in a single milking session. (4 points)

Part B A small dairy farm has 20 of these types of cows. Calculate the probability that the total volume for one milking session for these 20 cows exceeds 50 gallons. (8 points)

Part C Did you need to know that the population distribution of milk volumes per milking session was Normal in order to complete Parts A or B? Justify your answer. (8 points)