A farmer is interested in knowing the mean weight of his chickens when they leave the farm. Suppose that the standard deviation of the chickens’ weight is 500 grams.

(a) What is the minimum number of chickens needed to ensure the a standard deviation of the mean is no more than 100 grams with a confidence level of 0.95?

(b) If the farm has three coops and the mean chicken weight in each coop is 1.8, 1.9, and 2 kg, respectively, calculate the probability that a random sample of 50 chickens with an average weight larger than 1.975 kg comes from the first coop. Assume the weight of the chickens follows a normal distribution.

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