Although most of us buy milk by the quart or gallon, farmers measure daily production in pounds. Ayrshire cows average 55 pounds of milk a day, with a standard deviation of 6 pounds. For Jersey cows, the mean daily production is 52 pounds, with a standard deviation of 5 pounds. Assume that Normal models describe milk production for these breeds.
a) We select an Ayrshire at random. What's the probability that she averages more than 58 pounds of milk a day?
b) What's the probability that a randomly selected Ayrshire gives more milk than a randomly selected Jersey?
c) A farmer has 20 Jerseys. What's the probability that the average production for this small herd exceeds
54 pounds of milk a day, assuming they can be treated as a random sample of all Jersey cows?
d) A neighboring farmer has 10 Ayrshires. What's the probability that his herd average is at least 5 pounds higher than the average for part c's Jersey herd?