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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?

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Category:- Statistics and Probability
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