1. The volume of the milk produced in a single milking session by a certain breed of cow is Normally distributed with mean 2.3 gallons with a standard deviation of 0.96 gallons.

Part A Calculate the probability that a randomly selected cow produces between 2.0 gallons and 2.5 gallons in a single milking session. (4 points)

Part B A small dairy farm has 20 of these types of cows. Calculate the probability that the total volume for one milking session for these 20 cows exceeds 50 gallons. (8 points)

Part C Did you need to know that the population distribution of milk volumes per milking session was Normal in order to complete Parts A or B? Justify your answer. (8points)

2. An opinion poll asks a sample of 300 adults (an SRS) whether they favor giving parents of school-aged children vouchers that can be exchanged for after school activities at an organization of their choice. Each organization would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 37% of the population favor this idea.

Part A What is the mean of the sampling distribution of p, the proportion of adults in samples of 300 who favor giving parents of school-aged children these vouchers? (3 points)

Part B What is the standard deviation of p? (5 points)

Part C Check that you can use the Normal approximation for the distribution of p. (6points)

Part D What is the probability that more than half of the sample are in favor? Show your work. (6 points)