# MATHEMATICS

31. A normal population has a mean of 22 and a standard deviation of 5. (a) Compute the z value associated with 25 (Round your answer to 2 decimal places.) Z (b) What proportion of the population is between 22 and 25? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion (c) What proportion of the population is less than 18? (Round z-score computation to 2 decimal places and your final answer to 4 decimal places.) Proportion 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 3