Our statistics students, as noted were asked to rate their admiration of Hillary Rodham Clinton on a scale of 1 to 7. They also were asked to rate their admiration of Jennifer Lopez and 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 her z score for her admiration rating of Clinton?

b. What is her z score for her admiration rating of Williams?

c. What is her z score for her admiration 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 them?)

To calculate the z scores for each admiration rating, we can use the formula:

z = (x - μ) / σ

Where:
- x refers to the value or observation (in this case, the rating)
- μ refers to the mean of the population (in this case, the mean ratings of each celebrity)
- σ refers to the standard deviation of the population (in this case, the standard deviations of each celebrity)

a. For Clinton:
x = 5
μ = 4.06
σ = 1.70

Plugging in the values:
z = (5 - 4.06) / 1.70
z = 0.553

The z score for her admiration rating of Clinton is approximately 0.553.

b. For Williams:
x = 5
μ = 4.58
σ = 1.46

Plugging in the values:
z = (5 - 4.58) / 1.46
z = 0.287

The z score for her admiration rating of Williams is approximately 0.287.

c. For Lopez:
x = 4
μ = 3.72
σ = 1.90

Plugging in the values:
z = (4 - 3.72) / 1.90
z = 0.147

The z score for her admiration rating of Lopez is approximately 0.147.

d. To determine which celebrity she most admires compared to the other statistics students, we need to compare her z scores. A higher z score indicates a higher rating compared to the mean, while a lower z score indicates a lower rating compared to the mean.

In this case, the student's z score for Clinton (0.553) is higher than her z score for Williams (0.287) and Lopez (0.147). Therefore, this student most admires Hillary Rodham Clinton compared to Jennifer Lopez and Venus Williams.