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Review Questions Chapter 2
1. 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
2. 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
3. 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
4. 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
5. Given N(544, 103) find the score at the upper quartile
a) 1
b) 475
c) 470
d) 0
e) 613
6. 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
7. 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.
8. Find the proportion of runners who finish in less than 43 minutes.
9. Find the proportion of runners who take more than 70 minutes to finish.
10. 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.
11. 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.
12. 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
13. 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
14. 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
15. 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
16. 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%
17. 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
18. 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
19. 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 2 Key
1.
2.
3.
4.
5.
6.
E
c
b
a
e
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.
7. 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.
8. P(x<43) = P(z<(43-61)/9) ) = P(z< -2.00) = .0228
9. P(x>70) = P(z>(70-61)/9)) = P(z>1.00) = 1-.8413 =.1587
10. True.
11. A
12. D. 19.99 to 20.01 mm (Add and subtract one standard deviation from the mean)
13. A. a. 19.98 to 20.02 mm (Add and subtract two standard deviations from the
mean)
14. C. 1-.95 = .05.
15. D.88th percentile; Look in Table A.
16. A. 64%: .9192-.2743 from Table A.
17. E.
18. C. 95%: Mean + 2 standard deviations = 220; Mean = 2 standard deviations =
100. 2 Std. devs captures 95% of the data.
19. D