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. 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.

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. Part B:What is the shape of the sampling distribution of x? Justify your answer. 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.

3. An ecological group suspects dolphins are consuming dangerous levels of arsenic in a region of the world. Dangerous levels of arsenic are classified when they reach beyond 7.0 parts per million. A random sample of 28 dolphins in the region were tested and the data is shown in the stem plot. Key: 2|4 = 2.4 parts per million Part A:What proportion of the dolphins in the sample have dangerous levels of arsenic in their systems?

Part B:Construct and interpret a 99% confidence interval for the mean arsenic levels of the dolphins if the sample of 28 dolphins has a mean arsenic level of 5.26 parts per million and standard deviation of 1.49 parts per million.