Download 1. Variables can be divided into two types: a) Reasonable and

Review Questions Chapter P/1/2
1. Variables can be divided into two types:
a) Reasonable and Unreasonable
b) Categorical and Distributive
c) Quantitative and Qualitative
d) Categorical and Quantitative
2. The overall pattern of distribution is described by (pick any/all that apply):
a) spread
b) time plot
c) shape
d) variables
e) center
3. What is the difference between skewed left and skewed right?
4. The value of a stock started at $4.15 in January and by December it was worth
$2.12. The best way to give a visual display is to use a
______________________.
Here are the weights (in pounds) of 20 steers on al1 experimental feed diet:
183 140
136
142
172
153
172
156
70
167
192 166
113
171
178
159
129
112 135
174
5. Make a stemplot of this data.
6. Where is the center of the distribution of this data set?
7. Describe the overall pattern of distribution? (in other words, give a complete
description of the data)
In a survey of urban crime, 200 inhabitants of a city were asked the number of times they
had been a victim of street crime in the preceding five year's. Here is the frequency
distribution of the number of incidents:
No. of incidents
Frequency
0-3
154
4-7
24
8 - 11
18
12 -15
4
8. What is the class width?
9. Extend the table above by computing the relative class frequencies for each class.
The distribution of the ages of a nation's population has a strong influence on economic and
social conditions. The following table shows the age distribution of U.S. residents in 1950 and in
2075, in millions of persons. The 1950 data collected from that year's census, while the 2075 data
are projections made by the Census Bureau.
Age Group (yrs)
1950
2075
Under 10
29.3
34.9
10- 19
21.8
35.7
20- 29
24.0
36.8
30- 39
22.8
38.1
40- 49
19.3
37.8
50 59
15.5
37.5
60- 69
11.0
34.5
70- 79
5.5
27.2
80- 89
1.6
18.8
90- 99
0.1
7.7
100- 109
---1.7
Totals
151.1
310.6
10. In the left grid below, make a histogram of the 1950 age distribution. In the right
grid, make a histogram of the projected age distribution for year 2075. Be sure to
properly label each grid.
11. Describe the main features of the 1950 distribution.
12. What are the most important changes in the U.S. age distribution projected for
the125 year period between 1950 and 2075?
13. What two population parameters determine the shape of a normal curve? (They make a
normal curve tall and skinny or short and fat.)
a. median and mean
b. mode and standard deviation
c median and standard deviation
d. mean and mode
e. mean and standard deviation
14. Suppose a population of individuals has a mean weight of 160 pounds, with a population
standard deviation of 30 pounds. According to the empirical rule, what percent of the population
would be between 100 and 220 pounds?
a. 10%
b. 68%
c. 95%
d. 99.7%
e. None of the above
15. Given N(544, 103) What is the approximate percentage of scares between 500 and 700?
a) 50
b) 60
c) 70
d) 80
e) 90
16. Given N(544, 103) what is the approximate percentage of applicants who scored above a 450?
a) 82
b) -82
c) 26
d) 11
e) 1
17. Given N(544, 103) find the score at the upper quartile
a) 1
b) 475
c) 470
d) 0
e) 613
18. To the nearest whole number, what percentile is associated with z=-.68?
a) 10th percentile
b) 40th percentile
c) 50th percentile
d) 25th percentile
e) 75th percentile
19. A z-score is called a standardized score because you can:
A. translate any x-value into a z-score.
B. translate any x-value from a normal distribution into a z-score.
C. translate z-scores into a proportion, a percentile, or a probability of the normal
curve.
D. use z-scores to find the area between a z-score and the mean, or the area below
a z-score.
E. use them to compare x-values! to a universal standard, in this case, the standard
normal distribution.
Use the following information to answer Questions 8 and 9: Runner’s World reports that the
times of the finishers in the New York City 10-km run are normally distributed with a mean of 61
minutes and a standard deviation of 9 minutes.
20. Find the proportion of runners who finish in less than 43 minutes.
21. Find the proportion of runners who take more than 70 minutes to finish.
22. True or False: In a normal distribution, the mean, median, and mode all have the same
value and the graph of the distribution is symmetric.
23. In terms of std deviations, where are the inflection points in a normal curve?
a. 1 std deviation left AND 1 std deviation right of the mean
b. 1 std deviation left AND 2 std deviations right of the mean
c. 2 std deviations left AND 2 std deviations right of the mean
d. At the mean and median value
e. Halfway between the mean and the two most extreme outliers.
Use the following information for Questions 12 and 13: A population of bolts has a mean
thickness of 20 mm, with a population standard deviation of .01 mm.
24. Give, in mm, a min and max thickness that includes 68% of the population of bolts.
a. 20.00 to 20.02 mm
b. 19.00 to 21.00 mm
c. 19.98 to 20.02 mm
d. 19.99 to 20.01 mm
e. 19.97 to 20.03 mm
25. Give in mm, a min and max thickness that will include 95% of the population of
bolts.
a. 19.98 to 20.02 mm
b. 19.99 to 20.01 mm
c. 19.97 to 20.03 mm
d. 19.80 to 20.20 mm
e. These can’t be accurately computed
26. Using the empirical rule, you can assume that what percent of the normal distribution
is outside two standard deviations of the mean in either direction?
a. 50%
b. 10%
c. 5%
d. 1%
e. Can’t be decided
27. To the nearest whole number, what percentile is associated with z = + 1.2?
A. 25th percentile
B. 50th percentile
C.75th percentile
D.88th percentile
E. 12th percentile
28. What area, to the nearest whole percent, of the normal curve is located between z = 0.6 and z = +1.4?
A.
B.
C.
D.
E.
64%
91%
27%
50%
95%
29. What two population parameters determine the shape of a normal curve? (They make
a normal curve tall and skinny or short and fat.)
a. median and mean
b. mode and standard deviation
c median and standard deviation
d. mean and mode
e. mean and standard deviation
30. Suppose a population of individuals has a mean weight of 160 pounds, with a
population standard deviation of 30 pounds. According to the empirical rule, what
percent of the population would be between 100 and 220 pounds?
a. 10%
b. 68%
c. 95%
d. 99.7%
e. None of the above
31. Assume that normal curve A and normal curve B have identical population means.
Assume further than A has a greater population std. Deviation than B. Which curve is
taller, and why?
a. Curve A is taller because it has fewer inflection points
b. Curve A is taller because smaller std. Deviations produce wider curves.
c. Curve B is taller because its median is greater.
d. Curve B is taller because smaller std. Deviations produce thinner curves.
e. The curves are the same height
Review Questions Chapter P/1/2 Key
1. D
2. A, C, E
3. Use the definitions and show with graphs. Talk about where the majority of the data is!
4. Time plot
5.
6. 159 if you exclude the outlier, 157.5 = median
7. Skewed left, has a gap between 70-112, has an outlier of 70 (prove with IQR rule), a spread of
70-192) ; note: it’s only okay to say 112-192 with outlier
8. 4 units
9. Relative frequencies: 77, 12, 9, and 2%
10. Scale and label histograms
11. Non-symmetric, skewed right, spread (range) 0-99, center in the thirties. There is a large
proportion of children and young adults.
12. Center moved to the right (from 30’s to 40’s), there are more older people, more people
overall in 2075 (more people in each age group).
13. E
14. c
15. b
16. a
17. e
18.
D. the 25th percentile. From the normal curve table, you find that the closest area
to .2500 is associated with a z-score of -0.68.
19. e. Use them to compare x-values to a universal standard, in this case, the standard
normal distribution. By converting an x-value into a z-score, you are translating it to a
quantity with units in standard deviations rather than units of inches or pounds, for
example. This allows you to compare your x-values, in the form of z-scores, to a
universal standard, which is why we say that z-scores are standardized scores.
20. P(x<43) = P(z<(43-61)/9) ) = P(z< -2.00) = .0228
21. P(x>70) = P(z>(70-61)/9)) = P(z>1.00) = 1-.8413 =.1587
22. True.
23. A
24. D. 19.99 to 20.01 mm (Add and subtract one standard deviation from the mean)
25. A. a. 19.98 to 20.02 mm (Add and subtract two standard deviations from the
mean)
26. C. 1-.95 = .05.
27. D.88th percentile; Look in Table A.
28. A. 64%: .9192-.2743 from Table A.
29. E.
30. C. 95%: Mean + 2 standard deviations = 220; Mean = 2 standard deviations =
100. 2 Std. devs captures 95% of the data.
31. D