CHAPTER 8 Quiz Key
1.
Name:
Are all frequency curves bell-shaped? If yes, explain why. If no, give an example of one that is not.
ANSWER: NO. EXAMPLES: ANY REASONABLE ANSWER OK, SUCH AS A CURVE
THAT IS SKEWED TO THE LEFT OR RIGHT.
Narrative: Snake lengths
Suppose the lengths of a certain species of snake have a normal distribution with a mean of 45 inches.
2.
{Snake lengths narrative} Draw a picture of the distribution of snake lengths for this population.
ANSWER: A NORMAL CURVE WITH A MEAN OF 45 INDICATED.
3.
{Snake lengths narrative} What percentage of the snakes in this population are 45 inches long or
longer?
ANSWER: 50%
4.
What is another term for measurements following a ‘normal distribution’?
a. The measurements follow a ‘bell-shaped curve.’
b. The measurements follow a ‘normal curve.’
c. The measurements follow a ‘Gaussian curve.’
d. All of the above
ANSWER:
D
5.
Which of the following describes the entire area underneath a frequency curve?
a. The entire area is 1 or 100%.
b. The entire area is equal to the total number of individuals in the population.
c. The entire area is equal to the total percentage of individuals in the population with the
measurement being studied.
d. None of the above.
ANSWER:
A
6.
The bell-shaped frequency curve is so common that if a population has this shape, the measurements
are said to follow a __________ distribution.
ANSWER: NORMAL
7.
With a frequency curve, to figure out what percentage or proportion of the population falls into a
certain range, you have to figure out the __________ under the curve over that range.
ANSWER: AREA
8.
Nature provides numerous examples of populations of measurements that, at least approximately,
follow a normal curve. Give one example.
ANSWER: ANY REASONABLE ANSWER OK. EXAMPLES: IQ, STANDARDIZED TEST
SCORES, PHYSICAL MEASUREMENTS WITHIN A HOMOGENEOUS POPULATION.
9.
Which of the following measurements likely has a normal distribution, at least approximately?
a. Weights of 10-year old boys.
b. IQ scores of 12 graders.
c. Nationwide scores on the SAT (Scholastic Achievement Test).
d. All of the above.
ANSWER:
D
10. Which of the following describes measurements that have a normal distribution?
a. The majority of the measurements are somewhere close to the average.
b. The farther away you move from the average, the fewer individuals will have those more
extreme values for their measurements.
c. The mean of the measurements is located in the middle of the bell-shaped curve.
d. All of the above.
ANSWER:
D
11. Suppose you took a standardized test and the scores had a bell-shaped distribution. You only need
three pieces of information in order to find your percentile in the population of test scores. What are
those three pieces of information?
ANSWER: 1) YOUR TEST SCORE; 2) THE MEAN OF THE POPULATION OF TEST
SCORES; AND 3) THE STANDARD DEVIATION OF THE POPULATION OF TEST
SCORES.
Narrative: Entrance exam
Suppose a certain college has its own entrance exam, and scores on this exam follow a normal distribution
with mean 150 and standard deviation 20.
12. {Entrance exam narrative} Bob’s score on this exam was 130. What is Bob’s standard score, and
what does this mean in terms of where he stands in this population?
ANSWER: -1. BOB’S SCORE IS 1 STANDARD DEVIATION BELOW THE MEAN.
13. {Entrance exam narrative} Bob’s score on this exam was 130. What was Bob’s percentile, and what
does this mean in terms of how he compares to the rest of the population?
ANSWER: 16TH PERCENTILE. 16 PERCENT OF THE STUDENTS SCORED LOWER
THAN BOB, AND 84 PERCENT OF THE STUDENTS SCORED HIGHER THAN BOB.
14. {Entrance exam narrative} Sue’s standard score on this exam was −1.5. What was her original score?
ANSWER: 120.
15. Suppose your score on the GRE (Graduate Records Exam) was at the 90th percentile. What does that
mean?
a. You got 90% of the questions right.
b. 90% of the other students scored lower than you did.
c. 10% of the other students scored lower than you did.
d. None of the above.
ANSWER:
B
16. Which of the following is not true about a standard normal curve?
a. It is symmetric.
b. It has a mean of 0 and standard deviation of 1.
c. Its measurements are z-scores.
d. All of the above are true.
ANSWER:
D
17. Suppose one individual in a certain population had a z-score of −2. Which of the following is true?
a. This is a good thing because the individual is above average.
b. This individual’s measurement is 2 standard deviations below the mean.
c. This individual’s original measurement was a negative number.
d. All of the above are true.
ANSWER:
B
18. {Entrance exam narrative} [Normal table or calculator required.] Bob’s original score was 130 and
Jill’s standard score was +1.5. What percentage of the students taking this exam had scores that fell
between Bob and Sue’s scores?
a. 16%
b. 93%
c. 77%
d. Not enough information to tell.
ANSWER:
C
19. Your __________ in a population represents the position of your measurement in comparison with
everyone else’s.
ANSWER: PERCENTILE
20. A(n) __________ represents the number of standard deviations the observed value or score falls
above or below the mean.
ANSWER: STANDARD SCORE (OR Z-SCORE)
21. The Empirical Rule says that for a normal curve, approximately 68% of the values fall within 1
standard deviation of the mean in either direction, while 95% of the values fall within 2 standard
deviations of the mean in either direction. Explain why you don’t have twice as many values within 2
standard deviations as you do within 1 standard deviation.
ANSWER: BECAUSE OF THE NORMAL, OR BELL-SHAPED CURVE. THE MAJORITY
(68%) FALL CLOSE TO THE MEAN, WHERE THE “BELL” PART OF THE CURVE IS.
AS YOU MOVE AWAY, YOU GET INTO THE TAILS OF THE CURVE, WHICH
CONTAIN LESS AREA.
Narrative: Men’s heights
Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about
3 inches. Assume men’s heights follow a normal curve.
22. {Men’s heights narrative} Using the Empirical Rule, approximately what percentage of adult males
are under 64 inches tall?
ANSWER: 2.5%.
23. {Men’s heights narrative} Using the Empirical Rule, approximately what percentage of adult males
are between 64 and 73 inches tall?
ANSWER: 81.5%.
24. {Men’s heights narrative} Using the Empirical Rule, approximately what percentage of adult males
are below 73 inches tall?
ANSWER: 84%.
25. {Men’s heights narrative} Using the Empirical Rule, 95% of adult males should fall into what height
range?
a. They should be between 64 and 76 inches tall.
b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or
minus 2 standard deviations.
c. They should be at or below the 95th percentile, which is 74.92 inches.
d. None of the above.
ANSWER:
A
26. {Men’s heights narrative} Using the Empirical Rule, 68% of adult males should fall into what height
range?
a. Between 67 and 73 inches tall.
b. At or below 68 inches tall.
c. Between 70 and 73 inches tall.
d. None of the above.
ANSWER:
A
27. What do you need to check for first, before using the Empirical Rule to describe a population?
a. You need to check whether or not the population is large.
b. You need to check whether or not the population is Empirical.
c. You need to check whether or not the population follows a bell-shaped curve.
d. None of the above. The Empirical Rule works for any population.
ANSWER:
C
28. Suppose a population generally follows a normal curve, except that one of the measurements on this
curve falls more than 3 standard deviations above the mean. What would you call this value?
a. An extreme outlier.
b. An error. All the values should lie within 3 standard deviations of the mean.
c. A value that has a 99.7% chance of occurring, because of the Empirical Rule.
d. None of the above.
ANSWER:
A
29. Some easy-to-remember intervals can give you a picture of where the values on any normal curve
will fall. This information is known as the __________.
ANSWER: EMPIRICAL RULE
30. For any normal curve, almost all of the values will fall within __________ of the mean.
ANSWER: THREE STANDARD DEVIATIONS