Our statistics students were asked to rate their admiration of Hillary Clinton on a scale of 1 to 7. They also were asked to rate their admiration of actor, singer, and former American Idol judge Jennifer Lopez and their admiration of tennis player Venus Williams on a scale of 1 to 7. As noted earlier, the mean rating of Clinton was 4.06, with a standard deviation of 1.70. The mean rating of Lopez was 3.72, with a standard deviation of 1.90. The mean rating of Williams was 4.58, with a standard deviation of 1.46. One of our students rated her admiration of Clinton and Williams at 5 and her admiration of Lopez at 4. 

a. What is the student’s z score for her rating of Clinton?

b. What is the student’s z score for her rating of Williams? 

c. What is the student’s z score for her rating of Lopez? 

d. Compared to the other statistics students in our sample, which celebrity does this student most admire? (We can tell by her raw scores that she prefers Clinton and Williams to Lopez, but when we take into account the general perception of these celebrities, how does this student feel about each one?) 

e. How do z scores allow us to make comparisons that we cannot make with raw scores? That is, describe the benefits of standardization.