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Chapter 9 Review Problems Problem #1 Jack is taking Math 110 this semester and wants to evaluate his progress using data from quizzes he has taken so far. His quiz scores are as follows: 75, 80, 60, 90, 100, 40, 75, 95, 60, 75. Find the following: a.) mean b.) median c.) mode d.) range e.) standard deviation Problem #2 The normal monthly temperatures (in degrees Fahrenheit) for the month of July is listed for 20 different U.S. cities. 95.1 95.7 77.1 83.4 90.9 81.0 79.4 88.3 78.9 87.2 85.6 96.2 89.5 79.8 77.3 93.3 90.8 86.1 88.7 79.8 Find the mean, median, and mode of this data. Problem #3 Using the employment information in the table at right for Omega Corporation, find the mean, mode, and estimated median of the grouped data. Years of Service Number of Employees 1–5 15 6 – 10 32 11 – 15 47 16 – 20 29 21 – 25 18 26 – 30 6 Problem #4 The following distribution of commuting distances was obtained for a sample of Mutual of Nebraska employees. Find the mean and standard deviation for the commuting distances. Distance (miles) Frequency 1.0 – 3.0 2 3.0 – 5.0 6 5.0 – 7.0 12 7.0 – 9.0 50 9.0 – 11.0 35 11.0 – 13.0 15 13.0 – 15.0 5 Problem #5 Find the percent of the total area under a normal curve that is contained in the interval between z = -1.95 and z = -.25. Problem #6 Find the z-score such that 3.5% of the total area is to the left of z. Problem #7 Find a z-score such that 4% of the total area is to the right of z. Problem #8 Computers are shut down for certain periods of time for routine maintenance, installation of new hardware, and so on. The down times for a particular computer are normally distributed with a mean of 1.5 hours and a standard deviation of 0.4 hour. What percentage of the down times exceed 2 hours? Problem #9 According to the November 1993 issue of Harper’s magazine, kids spend from 1200 to 1800 hours a year in front of the television set. Suppose the time spent by kids in front of the television set is normally distributed with a mean equal to 1500 hours and a standard deviation equal to 100 hours. What percentage spend between 1400 and 1600 hours? Problem #10 The length of useful life of a fluorescent tube used for indoor gardening is normally distributed. The useful life has a mean of 600 hours and a standard deviation of 40 hours. A company installs 10,000 of these fluorescent tubes. Find the approximate number of tubes that will: a.) last more than 700 hours. b.) last less than 600 hours. Answers (Solutions available in SSCC Library at the Reserve Desk.) 1.) 2.) 3.) mean = 75 median = 75 mode = 75 range = 60 standard deviation = 18.105 mean = 86.205 median = 86.65 mode = 79.8 mean = 13.714 mode = occurs in interval 11-15 years estimated mode = 13 median = occurs in interval 11-15 years estimated median = 13 Answers continued (Solutions available in SSCC Library at the Reserve Desk.) 4.) mean = 8.8 standard deviation = 2.369 5.) .3757 6.) z = -1.81 7.) z = 1.75 8.) 10.56% 9.) 68.26% 10.) a.) 62 tubes b.) 5000 tubes