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Statistics 2
Problems from past midterms: midterm 1
1.
(10 points) The men enrolled in a large physiology course had an average weight of 160
pounds and an SD of 25 pounds. Their weights followed the normal curve closely.
(a) About what percent of the men weighed between 180 and 200 pounds?
(b) Out of just those men—that is, the ones who weighed between 180 and 200 pounds—
about what percent weighed between 180 and 190 pounds?
2.
(10 points) A distribution table for family income is shown below. The class intervals
include the left endpoint but not the right. (The table is a much simplified version of
the 1991 income distribution of US families receiving a social security cheque.)
Income
Percentage
(in thousands of dollars)
(of families)
0
–
10
20
10
–
30
45
30
–
50
20
50 – 100
15
(a) Plot the histogram. Mark the horizontal and vertical scales carefully. Label the
axes.
(b) True or False, and explain: ‘The median is $20,000.”
3.
(5 points)
There are 300 students in a large physical education class. The instructor
gives everyone in the class a reaction time test and a physical dexterity test. The dex
terity test is scored out of 10 points. The averages for the class are as follows:
average reaction time:
382 milliseconds
average dexterity score: 7.4 points
The instructor compares two methods for predicting the dexterity score of someone in
the class:
Method 1:
Ignore any information about the person. Just use the average 7.4
points as the prediction.
Method 2:
Take the reaction time of the person, and use the regression
method to predict his or her dexterity test score.
The instructor works out the r.m.s. error for each method and finds that the two r.m.s.
errors are about equal to one another.
The correlation coefficient between reaction time and dexterity score (for the students in
the course) must be around:
–0.1
–0.5
–0.9
can’t tell without more information
Please circle your choice and then explain it.
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4.
(5 points)
The height and weight of a group of five men are shown in the table below:
Person
Height
Weight
A
67
158
B
69
162
C
70
160
D
71
154
E
73
166
Height is measured in inches and weight in pounds. One of these five men is going to be
picked somehow or other and a statistician must estimate the weight of that man–but
without being told the height. The statistician knows the numbers in the table.
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 Spring '03
 aldous
 Statistics, Probability, Human height, San Francisco Chronicle

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