1. A large university claims that distribution of SAT Math scores of their students has a mean of 460 and a standard deviation of 44.5. Calculate the probability that the average SAT Math score of a random sample of 60 students will be at least 480. (Use State/Plan/Do/Conclude)

2. An opinion poll asks a simple random sample of 500 adults whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 47% of the population favor this idea. What is the probability that more than half (50%) of the sample are in favor? (Use State/Plan/Do/Conclude)

3. A certain beverage company is suspected of underfilling its cans of soft drink. The company advertises that its cans contain, on average, 12 ounces of soda with standard deviation 0.35 ounce. For the questions that follow, suppose that the company is telling the truth.

(a) Can you calculate the probability that a single randomly selected can contains 11.9 ounces or less? If so, find the probability. If not, explain why you cannot.

(b) A quality control inspector measures the contents of a random sample of 100 cans of the company's soda and calculates the sample mean . What is the shape, mean and standard deviation of the sampling distribution of for samples of size n = 100?

(c) The inspector in part (b) obtains a sample mean of 11.9 ounces. Calculate the probability that a random sample of 100 cans produces a sample mean amount of 11.9 ounces or less. (you do NOT have to do the full State/Plan/Do/Conclude here)

(d) Given that the inspector found an average of 11.9 ounces in their sample, and the probability of that result that you found in part (c) (assuming the company is being truthful), would you conclude that the company is telling the truth about how much soda is in each can? Justify your answer.