Question 1 A random sample of 10 waiters in Weston, West Virginia, revealed the following hourly earnings, including tips: 19, 18, 15, 16, 18, 17, 16, 18, 20, and 14. (Units are dollars.) (i) If the hourly earnings are normally distributed , estimate with 95% confidence the mean hourly earnings for all waitresses in Iowa City. (ii) Interpret your confidence interval. Question 2 A production filling operation has a historical standard deviation of 6 ounces. When in proper adjustment, the mean filling weight for the production process is 50 ounces. A quality control inspector periodically selects at random 36 containers and uses the sample mean filling weight to see if the process is in proper adjustment. (i) State the null and alternative hypotheses. (ii) Using a test statistic, test the hypothesis at the 5% level of significance. Question 3 Scores of high school students on a national calculus exam were normally distributed with a mean of 86 and a standard deviation of 4. (Total possible points = 100.) (i) What is the probability that a randomly selected student will have a score of 80 or higher? (ii) What is the probability that a randomly selected student will have a score between 80 and 90?