Deck 5: The Normal Curve

Question 1

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%.

Answer 1

34.13%.

Question 2

Assuming 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 $\pm$ 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.

Answer 3

about 68% of the total area.

Question 4

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)never touch the horizontal axis.
D)maintain the same distance above the horizontal axis beyond the 3rd standard deviation.

Question 5

Unlike empirical distribution,the theoretical normal curve is

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

Question 6

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 7

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 8

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

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

Question 9

A defining characteristic of the normal curve is that it is

A)theoretical.
B)positively skewed.
C)negatively skewed.
D)perfectly nonsymmetrical.

Question 10

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 11

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 12

On all normal curves the area between the mean and $\pm$ 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 13

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 14

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 15

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

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

Question 16

By definition,the normal curve is

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

Question 17

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 18

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.

Question 19

Assuming a normal distribution of 1000 cases,how many cases will be within $\pm$ 1 standard deviations of the mean?

A)at least 500
B)about 3
C)about 680
D)it's impossible to estimate

Question 20

As the standard deviation of a normal distribution increases,the percentage of the area between $\pm$ 1 standard deviation will

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

Question 21

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 22

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 23

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 24

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 25

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 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

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 28

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 29

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 30

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 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 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 33

The probability that a randomly selected case will have a score beyond $\pm$ 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 34

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

Question 35

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 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

As used in the social sciences,probabilities are a type of ____ which can 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 38

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 39

The Z scores of two test scores are -1.17 and +2.38.To find the total area beyond 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 40

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 41

For the distribution of GPAs described in problem 1,what is the probability that a randomly selected student will have a GPA

Question 42

A sample of university students has an average GPA of 2.78 with a standard deviation of 0.45.If GPA is normally distributed,what percentage of the students has GPAs