statistics questions

Utts Chapter 8 Questions

1. Remember from Chapter 7 that the range for a data set is the difference between the maximum

and minimum values. Explain why it makes sense that the bell-shaped data set of a few hundred

values should have a range of about 4 to 6 standard deviations.

2. Suppose that you were told that scores on an exam in a large class you are taking had a mean

of 75 and a standard deviation of 10 points. Also the exam scores ranged from 50 to 100 and they

were approximately bell-shaped.

a. Suppose your score on the exam was 80. Explain why it is reasonable to assume that

your standardized score is about 0.5.

b. Based on the standardized score in part b, about what proportion of the class scored

higher than you did on the exam.

3. Math SAT scores for students admitted to a university are bell-shaped with a mean of 520 and

a standard deviation of 60

a. Draw a picture of these SAT scores, indicate the cut-off points for the middle 68%, 95%,

and 99.7% of the scores.

b. A student had a math SAT score of 490. Find the standardized score for this student and

draw where her score would fall on your picture in “a.” above.

4. Give an example of a population of measurements that would not be normally distributed for

each of the following reasons.

a. The measurement can only result in a small number of possible values, instead of the

continuum over a substantial range that is required for a normal distribution.

b. The measurement cannot go below 0, but is likely to be skewed to the right because it is

extremely high for a small subset of all individuals.

5. A graduate school program in Statistics will admit only students with quantitative reasoning

GRE scores in the top 30%. What is the lowest GRE score it will accept? (Recall that the mean is

151.3 and the standard deviation is 8.7, and round your answer to the nearest whole number.)