4. Although most of us buy milk by the quart or half gallon, farmers measure daily production in pounds. Ayreshire 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 the milk production for these breeds is normally distributed.

a. We select an Ayreshire at random. What is the probability that she produces more than 50 pounds of milk a day?

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

c. What is the probability that this herd of Jersey produces an average of less than 38 pounds of milk per day? 

d. A neighboring farmer has 10 Ayreshires. What is the probability that his herd has an average daily milk production greater than greater than 50 pounds.

e. What is the probability that the mean milk production of this herd of Ayreshires is within 10 pounds of the mean?