Deck 8: Bell-Shaped Curves and Other Shapes

Question 1

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 1

All of the above

Question 2

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 2

All of the above.

Question 3

For Question use the following narrative
Narrative: Grades
Suppose a professor sees that his students' exam scores do not follow a normal curve, but he decides to assign grades by "grading on a bell-shaped curve" anyway.
{Grades narrative} Explain how this procedure tends to distort the grades.

Answer 3

This procedure has a tendency to ARTIFICIALLY spread out clumps of students who are at the top or bottom of the scale, so that students whose scores were very close together may receive different letter grades.

Question 4

For Questions , use the following narrative
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.
{Entrance exam narrative} Sue's standard score on this exam was −1.5.What was her original score?

Question 5

For Questions , use the following narrative
Narrative: Snake lengths
Suppose the lengths of a certain species of snake have a normal distribution with a mean of 45 inches.
{Snake lengths narrative} What percentage of the snakes in this population are 45 inches long or longer?

Question 6

For Questions , use the following narrative
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.
{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?

Question 7

Nature provides numerous examples of populations of measurements that, at least approximately, follow a normal curve.Give one example.

Question 8

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.

Question 9

For Questions , use the following narrative
Narrative: Snake lengths
Suppose the lengths of a certain species of snake have a normal distribution with a mean of 45 inches.
{Snake lengths narrative} Explain what it means for the snake lengths to have a bell-shaped distribution (use words that a non-statistician would understand).

Question 10

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?

Question 11

In a frequency curve, how do you interpret the height of the curve at any particular point?

A)The number of individuals in the population having that particular measurement.
B)The proportion of individuals in the population having that particular measurement.
C)The height of the individuals in the population represented by that particular point.
D)None of the above.

Question 12

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.

Question 13

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.

Question 14

What is the best way to represent the shape of a large population of measurements?

A)A histogram
B)A frequency curve
C)A bell-shaped curve
D)None of the above

Question 15

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.

Question 16

Are all frequency curves bell-shaped? If yes, explain why.If no, give an example of one that is not.

Question 17

For Questions , use the following narrative
Narrative: Snake lengths
Suppose the lengths of a certain species of snake have a normal distribution with a mean of 45 inches.
{Snake lengths narrative} Draw a picture of the distribution of snake lengths for this population.

Question 18

The bell-shaped frequency curve is so common that if a population has this shape, the measurements are said to follow a __________ distribution.

Question 19

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.

Question 20

For Questions , use the following narrative
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.
{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?

Question 21

For Questions use the following narrative
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.
{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.

Question 22

For Questions use the following narrative
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.
{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.

Question 23

Your __________ in a population represents the position of your measurement in comparison with everyone else's.

Question 24

{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.

Question 25

For Questions use the following narrative
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.
{Men's heights narrative} Using the Empirical Rule, approximately what percentage of adult males are under 64 inches tall?

Question 26

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.

Question 27

A(n) __________ represents the number of standard deviations the observed value or score falls above or below the mean.

Question 28

For Questions use the following narrative
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.
{Men's heights narrative} Using the Empirical Rule, approximately what percentage of adult males are below 73 inches tall?

Question 29

Suppose one individual in a certain population had a z-score of −2.Which of the following is true?

A)This is a bad thing because the individual is below 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.

Question 30

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.

Question 31

For any normal curve, almost all of the values will fall within __________ of the mean.

Question 32

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 __________.

Question 33

For Questions use the following narrative
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.
{Men's heights narrative} Using the Empirical Rule, approximately what percentage of adult males are between 64 and 73 inches tall?

Question 34

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.