ABC 1. Researchers at Georgia State University investigated the personality characteristics of drug dealers in order to shed light on their motivation for participating in the illegal drug market. The sample consisted of 100 convicted drug dealers who attended a court- mandated counseling program. Each dealer was scored on the Wanting Recognition (WR) Scale, which provides a quantitative measure of a person's level of need for approval and sensitivity to social situations. (Higher scores indicate a greater need for approval.) The sample ofdrug dealers had a mean WR score of 39, with a standard deviation of 6. Assume the distribution of WR scores for drug dealers is mound shaped and symmetric. a) Give a range of WR scores that will contain about 95% of the scores in the drug dealer sample. b) What proportion ofdrug dealers will have WR scores above 51? c) Give a range of WR scores that will contain nearly all the scores in the drug dealer sample? d) What proportion ofdrug dealers would have a WR score between 27 and 39? e) What proportion of drug dealers would have a WR score of 33 and 51? Compare the z-scores to decide which of the following x values lie the greatest distance above the mean and the greatest distance below the mean: a) x: 100, u: 50,o=25 b) x=1,u=4,o=1 c) x: 0, u: 200,0: 100 d) x: 10,u=5,o= 3 . At one university, the students are given z-scores at the end of each semester, rather than traditional GPAs. The mean and standard deviation of all students' cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively. a) Translate each of the following z-scores to corresponding GPA scores: 2 = 2.0, 2 = -1.0, 2 = .5, z = -2.5. b) Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA? c) The president of the university wishes to graduate the top 16% of the students with cum laude honors and the 2.5% with summa cum laude honors. Ifthe distribution of GPAs g approximately mound shaped, where should the limits be set in terms of z-scores? What about GPAs? 4. Use the data set below to answer the following questions: a) Find the mean and standard deviation of the dataset. b) Find the z-scores of all the data points. Do any appear to be an outlier? c) Find the Five Number Summary for the Data Set. d) Find the IQR. e) Find the Lower and Upper Inner Fences. 1') Find the Lower and Upper Outer Fences. g) Are there any outliers using the fence method? h) Draw or use technology to construct a boxplot. 10 80 80 85 85 85 85 90 90 90 90 90 95 95 95 95 100 100