Test 1 Practice
1. The midterm grades (𝑥) and final grades (𝑦) of 250 students were recorded. Both grades are out of
100. They are summarized in the following table
∑ 𝑥𝑖
∑ 𝑦𝑖
∑ 𝑥𝑖2
∑ 𝑦𝑖2
∑ 𝑥𝑖 𝑦𝑖
15065 14842.5 962357.9 909494.5 933556.8
A. Compute the value of the correlation coefficient between 𝑥 and 𝑦. I.e., compute 𝑟.
B. Find the equation of the regression line with midterm grade as independent variable (the predictor) and
the final grade as dependent variable (response).
C. The midterm grades (𝑋) range from 5 to 99. Predict the final grade of a student who received 80 on
their midterm.
2. The following data set represents the number of new computer accounts registered during a random
sample of 10 days.
43, 37, 50, 51, 58, 105, 52, 45, 45, 10
A. Find the mean and the standard deviation.
B. Construct a boxplot for the data. List any outliers.
3. Police reports that 78% of drivers stopped on suspicion of drunk driving get a breath test (event A),
36% a blood test (event B), and 8% get neither of the tests.
A. What proportion gets at least one of the two tests?
B. What proportion gets a blood test but not a breath test?
C. What proportion gets both tests?
D. What proportion of suspected drivers who get a breath test also get a blood test?
E. Are events A and B independent? Why or why not?
4. The following are the times it takes a computer to save a file. Times are in seconds.
1, 1, 1.2, 1.2, 1.3, 1.4, 1.6, 1.6, 1.6, 1.7, 1.8, 1.9, 2, 2, 2, 2.5, 2.5, 2.6, 2.7, 2.8, 2.9
Draw a stem and leaf plot. Split each stem into 2.