Directions: Please answer all of the questions below. The point values for each problem are indicated in parentheses. Partial credit will be awarded if you show your work.

1. The September 24, 1995 issue of The Columbus Dispatch contained residential listings of all homes for sale in the Columbus area. The file p:\data\math\stats\homes.mtw contains the prices of homes listed with the HER realtor. Retrieve the file and answer the questions below.

(5) a. Is the distribution of home prices symmetric or skewed?
(6) b. List two measures of center for the prices of homes listed with HER.
(6) c. List two measures of spread for the prices of homes listed with HER.
(5) d. Which measure of spread do you prefer for this data? Provide a short rationale for your choice.
(5) e. Construct a normal probability plot and comment on whether or not you would be willing to use the normal model for this data.
(6) f. Recall that linear transformations are defined by x^* = a + bx. Give the values of a and b that would be used to transform the selling price in dollars, x, to the selling price in thousands of dollars, x^*.
(5) g. Suppose a real estate agent sells five homes in a month and the average price of the homes sold is $195,000. If the agent works strictly on commission and makes 3% of her total sales for the month, can you find the gross amount of her paycheck for this month?

2. Suppose that high school grade point averages for the class of 2000 are normally distributed with a mean of 3.3 and a standard deviation of 0.3.

(5) a. What percent of the students in the class of 2000 have gpa's below 2.7?
(5) b. How high must a student's gpa be for them to place in the top 5% of the class?
(5) c. What percent of the students in the class of 2000 have gpa's above 3.5?
(5) d. How low must a student's gpa be for them to place in the bottom 20% of the class?
(5) e. What percent of the students in the class of 2000 have gpa's between 2.85 and 3.65?

3. The file p:\data\math\stats\examsm6.mtw contains exams scores for Kenyon students enrolled in Math 6 several years ago. Column 1 contains scores on the second exam and column 2 contains scores on the final exam. Usually in the last week of classes many students approach me and ask me to predict (or help them predict) their grade on the final exam and their grade for the course. Retrieve the file and answer the questions below.

(5) a. Is the association between exam 2 scores and final exam scores positive or negative?
(3) b. Find the value of the correlation coefficient.
(6) c Find the least squares regression line for predicting final exam scores.
(3) d. Predict the final exam score for a student who received an 82 on exam 2.
(3) e. What is the value of the residual for the student who received an 86 on exam 2 and a 68.97 on the final exam?
(5) f. Does the least squares line do a "good" job at predicting final exam scores for the students in this course? Please explain in a sentence or two.

4.(20) Carefully describe how the standard deviation measures variability in a set of data. Your description should include the relationship between the sample variance and the standard deviation.