Deck 5: The Normal Curve

Question 1

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.

Answer 1

adding the areas between each Z score and the mean.

Question 2

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 answer choices.

Answer 2

D

Question 3

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%

Answer 3

A

Question 4

By definition, the normal curve is________.

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

Question 5

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 6

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 answer choices are possible, depending on the value of the mean.

Question 7

If a case has a Z score of 2.3, the standard deviation would be________.

A) 4.6
B) 1
C) 0
D) One cannot calculate it based on this information.

Question 8

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 9

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

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

Question 10

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 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 answer choices are possible.

Question 20

In a distribution of 150 test scores, the mean grade was an 82 and the standard deviation was 8. If a student scored a 93, what would their equivalent Z score be?

A) 1.13
B) -1.38
C) 0.68
D) 1.38

Question 21

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 22

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 23

Unlike empirical distribution, the theoretical normal curve is________.

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

Question 24

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 Z score Area.
a. less than 2.30
b. less than 2.00
c. more than 2.00
d. more than 3.00
e. between 2.50 and 3.50
f. between 2.00 and 2.50

Question 25

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 26

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 27

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 is impossible to estimate.

Question 28

In terms of construction, the normal curve is what kind of chart?

A) pie chart
B) line chart
C) histogram
D) bar chart

Question 29

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 30

A common real world application of the normal curve is________.

A) measuring income levels.
B) assigning exam grades.
C) setting government budgets.
D) None of the answer choices.

Question 31

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 32

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 33

For the distribution of GPAs described in problem 1, what is the probability that a randomly selected student will have a GPA Z score Probability
a. less than 3.40
b. less than 3.78
c. more than 3.50
d. more than 2.50
e. between 2.00 and 3.00
f. between 3.00 and 3.50

Question 34

Distributions of IQ scores are normally distributed because________.

A) the underlying quality being tested - intelligence - is normally distributed.
B) IQ tests are designed to generate approximately 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 35

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 36

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 37

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