Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Ayrshire cows average 47 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 43 pounds, with a standard deviation of 5 pounds. Assume that Normal models describe milk production for these breeds.

a. If we select an Ayrshire at random, what's the probability that she averages more than 50 pounds of milk a day?

b. A farmer has 20 Jerseys. What's the probability that the average production for this small herd exceeds 45 pounds of milk a day?

c. A farmer has 20 Ayrshires. There's a 99% chance each day that this small herd produces at least how many pounds of milk?