Deck 5: The Normal Curve

Question 1

The tails of the theoretical normal curve

A) intersect with the horizontal axis between the 4th and 5th standard deviation
B) intersect with the horizontal axis beyond the 5th standard deviation
C) extend infinitely in both directions
D) maintain the same distance above the horizontal axis beyond the 3rd standard deviation

Answer 1

extend infinitely in both directions

Question 2

For a normal distribution of 1000 cases, how many cases will be farther away from the mean than ± 3 standard deviations?

A) at least 500
B) about 3
C) 327
D) it's impossible to estimate

Answer 2

about 3

Question 3

On all normal curves the area between the mean and +1 standard deviation will be

A) about 34% of the total area
B) about 68% of the total area
C) about 95% of the total area
D) about 99% of the total area

Answer 3

about 34% of the total area

Question 4

The area beyond ± 2 standard deviations contains approximately what % of the area under the normal curve?

A) 75%
B) 50%
C) 99%
D) 5%

Question 5

Distributions of IQ scores are normally distributed because

A) the underlying quality being tested - intelligence - is normally distributed
B) IQ tests are designed to produce in normal distributions
C) there is no cultural bias in the tests
D) they reflect the natural distribution of intelligence: human beings are genetically programmed to have an average intelligence of about 100.

Question 6

The standardized normal distribution (or Z distribution) has

A) a mean of 0 and a standard deviation of 1
B) a mean of 1 and a standard deviation of 0
C) a mean equal to the average of the scores and a standard deviation equal to the mean
D) a mean of 1 and a standard deviation of 1

Question 7

The Z score table gives the area between a score and the mean. For a Z score of -1.00 that area (in percentages) is

A) 34.13%
B) -34.13%
C) 68.26%
D) -68.26%

Question 8

When an empirical normal distribution of scores is standardized

A) the mean will become 0
B) the standard deviation will become 1
C) each score will be converted to a Z score
D) all of the above

Question 9

If a Z score is + 1.00, then the value of the corresponding raw score would be

A) 0
B) the same as the mean of the empirical distribution
C) equal to the mean of the empirical distribution plus one standard deviation
D) probably a negative number

Question 10

A Z score of -2.00 indicates a score that lies

A) two standard deviation units to the right of the mean
B) two standard deviation units to the left of the mean
C) 0.5 of one standard deviation unit on each side of the mean
D) any of the above are possible depending on the value of the mean

Question 11

A Z score of +1.00 indicates a score that lies

A) one standard deviation unit to the right of the mean
B) one standard deviation unit to the left of the mean
C) 1/2 of one standard deviation unit on each side of the mean
D) any of the above are possible

Question 12

If a Z score is 0, then the value of the corresponding raw score would be

A) 0
B) the same as the mean of the empirical distribution
C) the same as the standard deviation of the empirical distribution
D) probably a negative number

Question 13

On all normal curves the area between the mean and ± 1 standard deviation will be

A) about 34% of the total area
B) about 68% of the total area
C) 50% of the total area
D) 99.9% of the total area

Question 14

Converting scores into Z scores standardizes the original distribution to units of the

A) median
B) standard deviation
C) mean
D) percentage

Question 15

On all normal curves the area between the mean and ± 2 standard deviations will be

A) about 34% of the total area
B) about 95% of the total area
C) less than 50% of the total area
D) about 68% of the total area

Question 16

For a normal distribution of 1000 cases, how many cases will be within ± 1 standard deviations of the mean?

A) No more than 500
B) about 3
C) about 680
D) it's impossible to estimate because all normal curves are different

Question 17

As the standard deviation of a normal distribution increases, the percentage of the area between ± 1 standard deviation will

A) increase
B) stay the same
C) decrease
D) become non-symmetrical

Question 18

By definition, the normal curve is

A) symmetrical
B) positively skewed
C) negatively skewed
D) empirical

Question 19

Unlike empirical distribution, the theoretical normal curve is

A) positively skewed
B) negatively skewed
C) bimodal
D) perfectly symmetrical

Question 20

A defining characteristic of the normal curve is that it is

A) theoretical
B) positively skewed
C) negatively skewed
D) perfectly non-symmetrical

Question 21

The probability that a randomly selected case will have a score beyond ± 1.00 standard deviation of the mean is

A) 0.6826
B) 0.5000
C) 0.3174
D) 1/2 of the area of 1 standard deviation

Question 22

The area between the mean and a Z score of +1.50 is 43.32%. This score is higher than _________ of the scores in the distribution.

A) 43.32%
B) 51.50%
C) 57.68%
D) 93.32%

Question 23

The Z scores of two test scores are - 1.17 and + 2.38. To find the total area between these two scores

A) add the column b areas together
B) subtract each score from the mean and divide the result by the standard deviation
C) add the column b area to the column c area
D) add the column c areas

Question 24

The area between a negative Z score and a positive Z score can be found by

A) subtracting the Z scores from each other
B) subtracting each Z score from the mean and adding the results
C) adding the Z scores and finding the area in the Z score table for the summed Z scores
D) adding the areas between each Z score and the mean

Question 25

To estimate probabilities, set up a fraction with the number of _________ in the numerator and the number of _________ in the denominator

A) successes, failures
B) possible outcomes, successes
C) failures, successes
D) successes, possible outcomes

Question 26

To find the area above a positive Z score or below a negative Z score you would

A) subtract the value of the Z score from the mean
B) use the "Area Beyond Z" column of the Z score table
C) add the value of the Z score to the area beyond the mean
D) add the area between the Z score and the mean to 100%

Question 27

Column c in the normal curve table lists "areas beyond Z". This is the area

A) below a positive Z score
B) above a negative Z score
C) between two positive Z scores
D) above a positive Z score

Question 28

A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders. The scores were normally distributed with a mean of 45 and a standard deviation of 7. What is the probability that a randomly selected case from the sample will have a score less than 38?

A) 0.4526
B) 0.5018
C) 0.5200
D) 0.1587

Question 29

The mean on a standardized test is 100 and the standard deviation is 35. Your score is 65. What percentage of the scores were higher than yours?

A) about 84%
B) no more than 50%
C) about 34%
D) about 16%

Question 30

To obtain the area below a positive Z score or above a negative Z score you would

A) subtract the value of the Z score from the mean
B) subtract the area in the "Area Beyond Z" column of the Z score table from 50%
C) add the value of the Z score to the area beyond the mean
D) add the area between the Z score and the mean to 50%

Question 31

What is the probability that a randomly selected case from a normally distributed distribution will have a score between -1.00 and the mean?

A) 0.34
B) 0.16
C) 0.50
D) 0.86

Question 32

The Z scores of two tests scores are + 1.2 and + 1.5. To obtain the area between these scores

A) subtract the Z scores and find the area of the difference in the Z score table
B) find the area between each score and the mean in the Z score table and then subtract the smaller area from the larger area
C) find the area between each score and the mean in the Z score table and then subtract the difference between them from 100%
D) find the area beyond each score in the Z score table and subtract the difference between the areas from the mean

Question 33

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If the variable is normally distributed, what is the probability that a randomly selected town will have a homicide rate greater than 14?

A) 0.34
B) 0.68
C) 0.50
D) 0.02

Question 34

As used in the social sciences, probabilities are a type of ___________ which vary from _____________ .

A) percentage, 0 to 1
B) fraction, 0 to 100
C) proportion, 0.00 to 1.00
D) Z score, 0 to infinity

Question 35

The area between the mean and a Z score of +1.50 is 43.32%. This score is less than _________ of the scores in the distribution.

A) 43.32%
B) 6.68%
C) 3.32%
D) 93.32%

Question 36

The area between two negative Z scores can be found by

A) adding the Z scores and finding the area below the total Z score
B) subtracting the Z scores and finding the total area above the total Z score
C) finding the area between each Z score and the mean and subtracting the smaller area from the larger
D) finding the area between each Z score and the mean and adding the areas

Question 37

The probability of getting a 1 in a single toss of a six sided die would be

A) 2 to 1
B) 60 to 1
C) 1 in 6
D) impossible to estimate with the information given

Question 38

If a case is randomly selected from a normal distribution, the score of the case will most likely be

A) equal to the mean in value
B) close to the mean in value
C) at least 1 standard deviation above the mean
D) at least 1 standard deviation below the mean

Question 39

The mean score on a final chemistry exam was 75, and the standard deviation of the scores was 5. If the distribution is normal and your score was 70, what percentage of the scores was lower than yours?

A) 15.87%
B) 30.00%
C) 34.13%
D) 50.00%

Question 40

What is the probability that a randomly selected case from the sample in the previous question would have a score of 52 or more?

A) 0.7500
B) 0.6826
C) 0.3413
D) 0.1587

Question 41

The text discusses an application of probability theory that involved

A) betting on horse races
B) casino gambling
C) cheating on final exams
D) betting on the outcome of the presidential election

Question 42

The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If the variable is normally distributed, what is the probability that a randomly selected town will have a homicide rate greater than 8?

A) 0.34
B) 0.68
C) 0.84
D) 0.01