# Mathematics

32. The mean of a normal probability distribution is 360; the standard deviation is 10. (a) About 68 percent of the observations lie between what two values? Value 1 Value 2 (b) About 95 percent of the observations lie between what two values? Value 1 Value 2 (c) Practically all of the observations lie between what two values? Value 1 Value 2 33. Customers experiencing technical difficulty with their internet cable hookup may call an 800 number for technical support. It takes the technician between 30 seconds to 15 minutes to resolve the problem. The distribution of this support time follows the uniform distribution. (a) What are the values for a and b in minutes? (Do not round your intermediate calculations. Round your answer to 1 decimal place.) a b (b-1) What is the mean time to resolve the problem? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Mean (b-2) What is the standard deviation of the time? (Do not round your intermediate calculations. Round your answer to 2 decimal places.) Standard deviation (c) What percent of the problems take more than 5 minutes to resolve? (Do not round your intermediate calculations. Round your answer to 2 decimal places. Omit the “%” sign in your response.) Percent % (d) Suppose we wish to find the middle 50 percent of the problem-solving times. What are the end points of these two times? (Do not round your intermediate calculations. Round your answers to 3 decimal places.) End point 1 End point 2 34. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $22 and 36 per share. What is the probability that the stock price will be: (a) More than $29? (Round your answer to 4 decimal places.) Probability (b) Less than or equal to $27? (Round your answer to 4 decimal places.) Probability 35. A survey is being planned to determine the mean amount of time corporation executives watch television. A pilot survey indicated that the mean time per week is 13 hours, with a standard deviation of 2.0 hours. It is desired to estimate the mean viewing time within one-quarter hour. The 90 percent level of confidence is to be used. How many executives should be surveyed? (Round up your answer to the next whole number.) Number of executives 36. A population is estimated to have a standard deviation of 8. We want to estimate the population mean within 2, with a 90 percent level of confidence. How large a sample is required? (Round up your answer to the next whole number.) Sample required is . 37 The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 380 viewers. After viewing the comedy, 200 indicated they would watch the new show and suggested it replace the crime investigation show. (a) Estimate the value of the population proportion. (Round your answer to 3 decimal places.) Estimated population proportion (b) Develop a 95 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.) The confidence interval is between and . 38. The U.S. Dairy Industry wants to estimate the mean yearly milk consumption. A sample of 29 people reveals the mean yearly consumption to be 55 gallons with a standard deviation of 22 gallons. (a-1) What is the value of the population mean? Population mean (a-2) What is the best estimate of this value? Estimate population mean (c) For a 90 percent confidence interval, what is the value of t? (Round your answer to 3 decimal places.) Value of t (d) Develop the 90 percent confidence interval for the population mean. (Round your answers to 3 decimal places.) Confidence interval for the population mean is and . (e) Would it be reasonable to conclude that the population mean is 52 gallons? 39. Bob Nale is the owner of Nale’s Quick Fill. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal distribution with a population standard deviation of 2 gallons. From his records, he selects a random sample of 63 sales and finds the mean number of gallons sold is 8.59. (Round your answers to 2 decimal places.) (a) The point estimate of the population mean is (b) The 95 percent confidence interval for the population mean is between and . 40 A sample of 10 observations is selected from a normal population for which the population standard deviation is known to be 4. The sample mean is 20. (Round your answers to 3 decimal places.) (a) The standard error of the mean is . (c) The 99 percent confidence interval for the population mean is between and . 41. The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of $290 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 70 one-bedroom apartments and finding the mean to be at least $2,100 per month? (Round z value to 2 decimal places and final answer to 4 decimal places.) Probability 42. A normal population has a mean of 57 and a standard deviation of 14. You select a random sample of 16. Compute the probability the sample mean is (Round z values to 2 decimal places and final answers to 4 decimal places): (a) Greater than 60. Probability (b) Less than 56. Probability (c) Between 56 and 60. Probability 43. Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. (a) We want to select a random sample of five dealers. The random numbers are: 19, 78, 28, 34, 32, 37, 45, 48, 79, 89, 11 and 45. Which dealers would be included in the sample? (Enter the numbers as they appear.) (c) A sample is to consist of every sixth dealer. The number 8 is selected as the starting point. Which dealers are included in the sample?