1.

Given a population mean of 27.1 with a standard deviation of 8.4 and a sample size of 10, answer these questions: Part A: What is the standard deviation of the sampling distribution of x? Show your work. (5 points) Part B: What does the sample size need to be if you want the standard deviation of the sampling distribution of x to be 2.8? Show your work. (5 points)

2. The amount people pay for cable service varies quite a bit, but the mean monthly fee is $142 and the standard deviation is $29. The distribution is not Normal. Many people pay about $76 for basic cable and about $160 for premium service, but some pay much more. A sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. Let x be the mean amount paid. Part A: What are the mean and standard deviation of the sample distribution of x? Show your work and justify your reasoning. (4 points) Part B: What is the shape of the sampling distribution of x? Justify your answer. (2 points) Part C: What is the probability that the average cable service paid by the sample of cable service customers will exceed $143? Show your work. (4 points)

4. Miranda, a quality assurance inspector at a frozen treat factory, checks for product quality using a random sample of 11 frozen treats from a batch of 41, with 22 grape popsicles and 19 cherry popsicles. Let p be the proportion of grape popsicles in the sample. Part A: Is the 10% condition met in this case? Justify your answer. (5 points) Part B: Is the Normal condition met in this case? Justify your answer. (5 points)