6. A random group of students was surveyed to determine how many months it has been since they population standard deviation of 4.2 months. last visited the dentist. The sample of 32 students gave a mean average of 16 months. Assume a a) Find a 95% confidence interval for the population mean number of months since students have seen the dentist. Write answer in a full sentence. b) Find a 99% confidence interval for the same value. Write answer in a full sentence. c) Determine the minimum required sample size to determine a 95% confidence interval to within 1 month of the population mean. 7. The weights of ice cream cartons produced by a Vermont manufacturer are normally distributed with a mean of 10 ounces and a standard devition of 0.6 ounces. a) What is the probability that a randomly selected carton has a weight less than 9.8 oz? b) You randomly select 33 ice cream cartons. What is the probability that their mean is less than 9.8 oz? c) Compare the answers for (a) and (b) and account for any differences. Use your sketches for each part in your explanations. d) Are either of your answers to (a) or (b) unusual? Explain how you know. 8. a) Explain this statement: "The mayor of a small town is reported to have a 67% approval rating with a margin of error of 5%." b) Give 2 ways to make a confidence interval smaller. 9. The financial aid office at a local college needs information about student loans. They surveyed 16 students and collected some data. The mean loan amount for this sample was $2486 with a standard deviation of $256. Assume the debt amounts are normally distributed. a) What distribution should be used to construct a confidence interval for the population mean? b) Clearly explain your choice and any conditions that apply. c) Find a 99% confidence interval for the population mean student debt. Write answer in a full sentence. 10. a) The amount of coffee dispensed by a machine is normally distributed with a mean of 9.8 oz. and a standard deviation of 0.12 oz. The size cup used in this machine is a 10 oz. cup. What percentage of cups will overflow with coffee? b) The coffee machine has a mean life of 1.4 years with a standard deviation of 0.3 years. The new owner of the company wants to guarantee the coffee machine so they replace no more than 4% of the coffee makers. What should the guarantee period be? 2