6.42 Percentiles and eating habits: As noted in How It Works 6.1, Georgiou and colleagues (1997) reported that college students had healthier eating habits, on average, than did those individuals who were neither college students nor college graduates. The 412 students in the study ate breakfast a mean of 4.1 times per week, with a standard deviation of 2.4. (For this exercise, again imagine that this is the entire population of interest.)

a.What is the approximate percentile for a student who eats breakfast four times per week?

b.What is the approximate percentile for a student who eats breakfast six times per week?

c.What is the approximate percentile for a student who eats breakfast twice a week?

6.44 z scores and comparisons of admiration ratings: 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.

6.46 Distributions and life expectancy: Researchers have reported that the projected life expectancy for South African men diagnosed with human immunodeficiency virus (HIV) at age 20 who receive antiretroviral therapy (ART) is 27.6 years (Johnson et al., 2013). Imagine that the researchers determined this by following 250 people with HIV who were receiving ART and calculating the mean.

a.What is the dependent variable of interest?

b.What is the population?

c.What is the sample?

d.For the population, describe what the distribution of scores would be.

e.For the population, describe what the distribution of means would be.

f.If the distribution of the population were skewed, would the distribution of scores likely be skewed or approximately normal? Explain your answer.

g.Would the distribution of means be skewed or approximately normal? Explain your answer.