Using scores for grades. At one university, the stademts are given z-scores Z end of each semester raher than the 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 cach of the following 2-4cores to the comesponding GPA:2.0,1.0,5, 25. b. Saudents with zscores below -16 are put on probation. What is the corresponding probationary GPA? e. The peesident of the university wishes to graduate the top 16% of the stadents with (approximately) should the limits be set in terms of 2-scores? In terms of GPAs? What asumpeion, if any, did you make about the distribution of the GPAS at the university?

The average chef at a restaurant earns $17 an hour with a deviation of $1.75. What are the chances that someone is earning more than $20 an hour?

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 77.977.9 Mbps. The complete list of 50 data speeds has a mean of x overbarxequals=17.5417.54 Mbps and a standard deviation of sequals=18.9718.97 Mbps.   a. What is the difference between​ carrier's highest data speed and the mean of all 50 data​ speeds? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert the​ carrier's highest data speed to a z score. d. If we consider data speeds that convert to z scores between minus−2 and 2 to be neither significantly low nor significantly​ high, is the​ carrier's highest data speed​ significant?

Suppose that the mean weight for men 18 to 24 years old is 170 pounds, and the standard deviation is 20 pounds. In each part, find the value of the standardized score (z-score) for the given weight. USE SALT (a) 206 pounds. Z = (b) 140 pounds. Z = (c) 173 pounds. Z = (d) 236 pounds. Z =