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Problem # 1 g 20 pts[. The lengths of lumber a machine cuts are normally distributed, with a mean of 96 inches and a standard deviation of 0.5 inch. (Hint: Pay attention to the difference in the two questions and decide which method to use). a) What is the probability that a randomly selected board cut by the machine has a length greater than 96.25 inches? b) You randomly select 40 boards. What is the probability that their mean length is greater than 96.25 inches? Problem # 2 g 20 pts!. Listed below are amounts of coffee (in ounces) randomly selected from different vending machines made by the Newton Machine Company. Use the sample results to construct a 95% condence interval for the mean amount of coffee in all dispensed cups. Assume that the population is normally distributed. 11.5 10.8 9.7 13.0 11.5 11.1 13.2 11.1 11.1 12.6 Hint: a) Find the sample mean and the sample standard deviation (You can use the sample computational formula to find 5). B) Use the tdistribution to nd the critical value. Recall that n is the size of the sample. C) Estimate the population mean. (See PPT slides in Module 10). Problem # 3 g 20 pts). The weekly time spent (in hours) on homework for 16 randomly selected college students. Assume that the population is normally distributed. 12.0 11.3 13.5 11.7 12.0 13.0 15.5 10.8 12.3 14.0 9.5 8.8 10.0 12.8 15.0 11.8 Use the sample results to construct a 90% confidence interval for the mean weekly time spent (in hours) on homework for the population. Hint: a) Find the sample mean and the sample standard deviation (You can use the sample computational formula to nd 5). B) Use the tdistribution to nd the critical value. Recall that n is the size of the sample, in this case 16. C) Estimate the population mean. (See PPT slides in Module 10). Problem # 4 g 20 pts! The manager of the dairy section of a large supermarket took a random sample of 250 egg cartons and found that 40 cartons had at least one broken egg. 3) Let p be the proportion of egg cartons with at least one broken egg out of the population of all egg cartons stocked by this store. Find a point estimate for p. b) Find a 90% confidence interval for p. Problem # 5 g 20 pts! A survey of 80 recent fatal trafc accidents showed that 46 were alcoholrelated. a) What is the best point estimate? b) Find the 95% confidence interval of the true proportion of fatal alcohol- related accidents