= 8 minutes and = 2 minutes.a. What is the probability that the sample mean is between 7.8 and 8.2 minutes?b. What is the probability that the sample mean is between 7.5 and 8 minutes?c. If you select a random sample of 100 sessions, what is the probability that t he sample mean is between 7.8 and 8.2 minutes?8. According to the National Restaurant Association, 20% of fine-dining restaurants have instituted policies restricting the use of cell phones. From a sample of 100 fine-dining restaurants, a. what is the probability that the sample has between 15% and 25% of restaurants that have established such policies?b. the probability is 90% that the sample percentage will be contained within what symmetrical limits of the population percentage?9.* The following data represent the service charge for direct-deposit customers if a customer’s account falls below the minimum required \$1,500 balance for a sample of 26 banks.9 7 10 7 75 5 9 a. Construct a 95% confidence interval for the population mean service charge if a customer’s account falls below the \$1,500 minimumb. Explain in words what this confidence interval means10. A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within plus-or-minus \$50 of the population mean. A previous study indicates that the standard deviation is approximately \$400.a. How large a sample size is needed?b. If management wants to be correct to within plus-or-minus \$25, what sample size is necessary?11. According to a poll conducted by American Express, 35% of people living in the United States use the Internet when planning their vacation. a. To conduct a follow-up study that would provide 95% confidence that the point estimate is correct to within plus-or-minus 0.04 of the population proportion, how large a sample size is required?b. To conduct a follow-up study that would provide 99% confidence that the point estimate is correct to within plus-or-minus 0.02 of the population proportion, how large a sample size is required?12. The director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth has a mean breaking strength of 70 pounds. A sample of 49 pieces of cloth reveals a sample mean breaking strength of 69.1 pounds. State the null and alternative hypotheses.