Posted: February 1st, 2021
1. Someone has sketched one block of a family-income histogram. About what percentage of families in this district had incomes between $60,000 and $75,000 a year?
2 % per $1,000
50 100
Family Income (in $1,000)
(10 points)
2. In a large lecture course, the scores on the final examination followed the normal curve closely. The average score was 50 points and three fourths of the class scored between 40 and 60 points. The SD of the scores was
(i) large than 10 points
(i) smaller than 10 points
(iii) impossible to say with the information given.
(15 points)
3. The weight of a certain group of men follow the normal curve, with an average of 160 pounds and an SD of 30 pounds. Fill in the blanks; explain briefly.
a. A man who weighed 120 pounds was at the ________percentile of the weight distribution.
b. To be at the 80^{th} percentile of the distribution, a man needed to weight about _________ pounds
c. About what percentage of these men weigh between 180 pounds and 200 pounds?
(20 points)
4. Given the following data set:
x |
1 |
3 |
7 |
9 |
13 |
15 |
y |
1 |
5 |
8 |
10 |
11 |
13 |
a. Find the correlation coefficient.
b. Using this to predict the value of y when x = 2.
c. Find the root mean square error.
(20 points)
5. For 1000 men age 18 – 24 in the HANES sample
Average height (X) = 70 inches SD_{x} = 3 inches
Average weight (Y) = 162 pounds SD_{y} = 30 pounds
Correlation r = .6
One man in the sample was 63 inches tall what is his expected weight?
(15 points)
6. In a certain class, midterm score average out 60 with an SD of 15, as do scores on the final. The correlation between midterm scores and final scores is about 0.50.the scatter diagram is football-shaped.
a. Predict the final score for a student whose midterm score is
(i) 75 (ii) 30 (ii) 60 (iv) unknown
b. Predict the midterm score for a student whose final score is 45.
c. Apparently low-scoring students on the midterm do better on the final, but low –
scoring student on the final did better on the midterm. How is this possible?
(20 points)
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