1. A quality control specialist for a restaurant chain takes a random sample of size 10 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.50 with a sample standard deviation of 1.54. Assume the underlying population is normally distributed.Find the 95% confidence interval for the true population mean for the amount of soda served. (Round your answers to two decimal places.(___,___)2. A quality control specialist for a restaurant chain takes a random sample of size 14 to check the amount of soda served in the 16 oz. serving size. The sample mean is 13.50 with a sample standard deviation of 1.57. Assume the underlying population is normally distributed. We wish to construct a 95% confidence interval for the true population mean for the amount of soda served. What is the error bound? (Round your answer to two decimal places.)3. A magazine published data on the best small firms in a certain year. These were firms that had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the corporate CEOs for a random sample of these firms.495950605659746353505960605746556357475557436162496767555549Use this sample data to construct a 90% confidence interval for the mean age of CEO’s for these top small firms. Use the Student’s t-distribution. (Round your answers to two decimal places.)(___,___)4. A survey organization, as part of the United States Census Bureau, conducts a yearly census similar to the one taken every ten years, but with a smaller percentage of participants. One of these surveys estimates with 90% confidence that the mean household income in the U.S. falls between $69,712 and $69,926. Find the point estimate for mean U.S. household income. (Enter your answer as a whole number.)x =Find the error bound for mean U.S. household income. (Enter your answer as a whole number.)EBM =5. Of 1,050 randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wage earners, 250 identified themselves as mid-level managers, and 160 identified themselves as executives. In the survey, 82% of manual laborers preferred trucks, 62% of non-manual wage earners preferred trucks, 54% of mid-level managers preferred trucks, and 26% of executives preferred trucks.We are interested in finding the 95% confidence interval for the percent of executives who prefer trucks. Which distribution should you use for this problem? (Round your answers to two decimal places.)p’ ~N (____,_____)6. A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.5; 2.9; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.NOTE: If you are using a Student’s t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)(i) Round your answer to two decimal places.x = sx=(II) Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)MathStatistics and Probability MATH MISC
