SOC 1167, Summer II Name:_______________________________ Assignment #5 Total points: _____ (out of 5) 1. The following scores were earned by ten students taking a final exam. For the entire class, the exam scores were normally distributed with a mean of 75pts. and a standard deviation of 8pts. Convert the student scores (points earned) on the final exam into Z scores 66, 98, 74, 83, 92, 51, 78, 87, 70, 95 = 66 98 74 83 92 51 78 87 70 95 2. Using the mean and standard deviation from Problem 1, find the raw score associated with the following Z scores: Z = 1.96 Z = 0.67 Z = -1.15 3. SAT scores are normally distributed. In 2010 the average SAT score was 1509 with a standard deviation of 312. Using the Standard Normal Table, what percentage of exam takers will score: a. Above 2200? b. Below 800? c. Between 1200 and 2000? 4. Workers at a large corporation are paid by the hour. Data from HR show that the distribution of hourly wages for all employees is normally distributed, with a mean of $12.00/hr and a standard deviation of $2.50/hr. Determine: a. the percentage of employees who earn a wage of $15 or more. b. the percentage of employees earning between $10/hr and $12/hr. c. the percentage of employees earning between $7.50/hr and $9.00/hr. d. the hourly pay representing the 75th percentile. 5. A researcher develops a scale for ranking universities and finds colleges measured an average score of 675pts and a standard deviation of 55pts (based on a 1,000-point scale) and that the scores are normally distributed. a) A university board of trustees votes to give the president a raise only if the college scores in the top 15 percentile. The university scores a 725. Will the president get a raise? b) The board also agrees that the president will be fired if they ever score below the 40 percentile. What score must the president keep the college above