A dairy farmer buys a heifer (female calf) from a Holstein-Friesian herd that is thought to be genetically superior to others in the region. The quantity of milk production among mature cows in the herd is normally distributed with µ = 18,000 lb/year and s = 2500 lb/year. Assuming the new owner can provide feed, shelter, and other environmental factors equivalent to those for the herd from which the calf was bought:
a. Give the numerical value of E(y), the expected milk production of the calf when it reaches maturity.
b. What is the probability that the calf will produce at a greater rate than the mean of the herd from which it was bought?
c. What is the probability that it will produce at a rate greater than the breed mean of µ = 14,000?