6.32 Normal distributions in real life: Many variables are normally distributed, but not all are. (Fortunately, the central limit theorem saves us when we conduct research on samples from non-normal populations if the samples are larger than 30!) Which of the following are likely to be normally distributed, and which are likely to be non-normal? Explain your answers.

a.In the population of students admitted to the highly selective University of Toronto, scores on the federal or provincial literacy test (required for university admissions)

b.In the population of secondary school students in New Zealand, the number of daily calories consumed

c.In the population of employed adults in San Antonio, Texas, the amount of time spent commuting to work

d.In the population of North American university students, the number of frequent flyer miles earned in a year

6.34 z scores and the GRE: By design, the verbal subtest of the GRE has a population mean of 500 and a population standard deviation of 100 (the quantitative subtest has the same mean and standard deviation).

a.Use symbolic notation to state the mean and the standard deviation of the GRE verbal test.

b.Convert a GRE score of 700 to a z score without using a formula.

c.Convert a GRE score of 550 to a z score without using a formula.

d.Convert a GRE score of 400 to a z score without using a formula.