Question 1

A person received a test score that was in the top 20% of everyone who has taken the test. The test scores are normally distributed. This person's Z score must be at least:
A).46
B).84
C)5.03
D)7.93

Accepted Answer

To be in the top 20%, the person's score must be greater than 80% of the scores. Using a z-table or calculator, we can find that the z-score corresponding to the 80th percentile is approximately 0.84. Therefore, the person's z-score must be at least 0.84 to be in the top 20%.

Question 2

John attained a score of 65 on his stats exam. The mean for the class was a 70 with a SD of 10. What percentage of students scored below and above John?
A)31 and 69
B)40 and 60
C)45 and 55
D)10 and 90

Accepted Answer

John's score is one-half standard deviation below the mean (since 65 is 5 points below the mean of 70, and the standard deviation is 10). In a normal distribution, about 34% of the data lies between the mean and one standard deviation below the mean. Since John's score is halfway to this point, approximately 34%/2 = 17% lie between him and the mean. Therefore, about 50% (the percentage below the mean) minus 17% equals 33% below John's score. Rounding and considering the empirical rule, approximately 31% scored below John and 69% scored above.

Question 3

The mean score on a creativity test is 20 and the standard deviation is 5. The distribution is normal. Using the percentage approximations for the normal curve, how many people would attain a score between 15 and 25?
A)34%
B)14% + 34% = 48%
C)50%
D)34% + 34% = 68%

Accepted Answer

To find the percentage of people who would attain a score between 15 and 25, we need to calculate the z-scores for these values.

For a score of 15: 
z = (15 - 20) / 5 = -1

For a score of 25: 
z = (25 - 20) / 5 = 1

Using a z-table or calculator, we can find that the percentage of individuals with a z-score between -1 and 1 is approximately 34% (or 0.34). Therefore, 34% of individuals would have a creativity score between 15 and 25.

However, we need to consider both sides of the normal curve, so we have to add the percentage of individuals with a z-score less than -1 to the percentage with a z-score less than 1.

The percentage of individuals with a z-score less than -1 is also approximately 34%.

Therefore, the total percentage of individuals with a creativity score between 15 and 25 is approximately 34% + 34% = 68%.

So, option D is the correct answer.

Question 4

What IQ score would a person need to be in the top 5% of the general population? Assume M = 100 and SD = 16.
A)110.45
B)115.44
C)120.05
D)126.24

Accepted Answer

To be in the top 5% of the population, a person needs to be above the 95th percentile. Using the standard normal distribution, the z-score for the 95th percentile is approximately 1.645. Using the formula IQ = M + z(SD), we calculate IQ = 100 + 1.645(16) = 126.24.

Question 5

The _____________ explains why many distributions tend to be close to normal in the real world.
A)central limit theorem
B)normal curve table
C)Pythagorean theorem
D)triples list calculation

Accepted Answer

The central limit theorem states that as sample size increases, the sampling distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This explains why many distributions tend to be close to normal in the real world.

Question 6

On a normal curve, what percentage of scores fall between a Z score of 1.29 and a Z score of 1.49?
A).54
B)3.04
C)1.85
D)6.05

Accepted Answer

The answer of On a normal curve, what percentage of...

Question 7

A person received a score of 4.78 on a test. This turned out to be a Z score of +1.5. What percentage are above this score? Assume a normal distribution.
A)43.32% - 50% = -6.68%
B)50% - 43.32% = 6.68%
C)100% - 43.32% = 56.68%
D)50% + 43.32% = 83.32%

Accepted Answer

A Z score of +1.5 corresponds to a percentile of 93.32%, which means that 6.68% of the scores are above it. To find the percentage above the score, we subtract this percentage from 50% (since the normal distribution is symmetric). Therefore, the percentage above the score is 50% - 6.68% = 43.32%.

Question 8

What Z score would a person need to be in the 4% of his or her class on a particular test? Assume a normal distribution.
A)4% - 50% = -46%, which corresponds to a Z score of -1.75
B)50% - 46% = 4%, which corresponds to a Z score of .10
C)50% - 4% = 46%, which corresponds to a Z score of 1.75
D)34% + 14% - 4% = 44%, which corresponds to a Z score of 1.55 or 1.56

Accepted Answer

To find the Z score for the top 4% of the class, we need to find the Z score that corresponds to the area to the right of the cutoff point (since we want the top 4%). Using a standard normal table or calculator, we find that the Z score that corresponds to an area of 0.04 to the right is approximately 1.75. Therefore, the answer is choice C.

Question 9

A person received a test score that is in the top 32% and the test scores follow a normal curve. This person's Z score must be at least:
A).46
B)1.5
C)2.8
D).91

Accepted Answer

A Z score of .46 corresponds to approximately the 32nd percentile from the top in a standard normal distribution.

Question 10

If you were looking at a graph of a normal distribution, which of the following would best describe it?
A)Bimodal and roughly symmetrical
B)Unimodal, roughly symmetrical, and bell-shaped
C)Skewed to the right
D)Roughly symmetrical and W-shaped

Accepted Answer

A normal distribution is unimodal, roughly symmetrical, and bell-shaped. It does not have multiple modes or a skewed shape. It also does not have a W-shape, which is characteristic of a bimodal distribution.

Question 11

Carrie attained a score of 650 on the verbal section of her SAT. The mean grade was a 500 with a standard deviation of 100. What percentage of test takers scored below and above Carrie?
A)85 and 15
B)10 and 90
C)93 and 7
D)more information is required to answer this question

Accepted Answer

Carrie's score is 1.5 standard deviations above the mean (650 - 500 = 150; 150 / 100 = 1.5). According to the empirical rule (or looking up a Z-table for a more precise value), approximately 93% of scores fall below a score that is 1.5 standard deviations above the mean, leaving about 7% scoring higher.

Question 12

The normal curve table shows percentages of scores:
A)between a correlation of -1 and +1
B)between a correlation of 0 and -1
C)between the median and various numbers of Z scores above the median
D)between the mean and various numbers of Z scores above or below the mean

Accepted Answer

The following question(s)may require use of a normal curve table.

Question 13

Using the percentage approximations for the normal curve, what percentage of scores are between the mean and one standard deviation below the mean?
A)14%
B)50% - 34% = 16%
C)34%
D)50%

Accepted Answer

34% of scores lie between the mean and one standard deviation below the mean on a normal distribution curve.

Question 14

A particular nation has a human rights score of 41, which equals a Z score of 1.3. What is the percentage of nations above this score? (Assume a normal distribution.)
A)40.32% - 50% = -9.68%
B)50% - 40.32% = 9.68%
C)100% - 40.32% = 59.68%
D)50% + 40.32% = 99.68%

Accepted Answer

Using a Z-table, a Z score of 1.3 corresponds to an area under the curve of 90.32%. Since we are looking for the percentage of nations above this score, we subtract 90.32% from 100%, which gives us 9.68%. Therefore, choice B is the correct answer.

Question 15

The mean score on a political attitude scale is 5 and the standard deviation is 2. The distribution is normal. Using the percentage approximations for the normal curve, how many people would get a score between 5 and 9?
A)34%
B)34% + 14% = 48%
C)50%
D)34% + 34% = 68%

Accepted Answer

Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean in a normal distribution. In this case, one standard deviation above the mean is 7 and one standard deviation below the mean is 3. Therefore, approximately 34% of the data falls between the mean of 5 and one standard deviation above the mean at 7. To find the percentage of people who scored between 5 and 9, we need to add the percentage of people who scored between the mean and one standard deviation above the mean (34%) with the percentage of people who scored between one standard deviation above the mean and two standard deviations above the mean (which is approximately 14%). This gives us a total of 48%, which is the closest answer choice.

Question 16

What Z score would a person need to be in the top 5%? Assume a normal distribution.
A)5% - 50% = -45%, which corresponds to a Z score of -1.64
B)-5%, which corresponds to a Z score of -.12
C)5%, which corresponds to a Z score of .12
D)50% - 5% = 45%, which corresponds to a Z score of 1.64

Accepted Answer

To be in the top 5% of a normal distribution, we need to find the Z score that corresponds to the area of 0.95 (since the top 5% is the same as the 95th percentile). Using a Z table, we can find that the Z score corresponding to the 95th percentile is approximately 1.64. Therefore, we would need a Z score of 1.64 or higher to be in the top 5%. Choice D is the correct answer.

Question 17

If a person has an IQ of 130, approximately what percentage of people have higher IQs? Assume M = 100 and SD = 16.
A)1%
B)3%
C)6%
D)9%

Accepted Answer

An IQ of 130 is 2 standard deviations above the mean (since the mean is 100 and the standard deviation is 16). In a normal distribution, about 2.5% of people score more than 2 standard deviations above the mean. However, since the question asks for the approximate percentage, the closest option given is 3%.

Question 18

Distributions observed in nature and research commonly approximate:
A)a kurtotic curve
B)a multimodal, symmetric curve
C)a normal curve
D)a bimodal, asymmetric curve

Accepted Answer

Distributions observed in nature and research often approximate a normal curve, also known as a Gaussian distribution, which is characterized by its symmetric, bell-shaped curve where most observations cluster around the central peak and the probabilities for values further away from the mean taper off equally in both directions.

Question 19

Jake's Z score for running ability is .60. What is Jake's raw score (assuming M =100 and SD = 7).
A)raw score = 100.1
B)raw score = 104.2
C)raw score = 93.5
D)raw score = 103.2

Accepted Answer

Z score formula: (X - M) / SD

0.60 = (X - 100) / 7   (substituting given values)

0.60 * 7 = (X - 100)

4.2 + 100 = X

X = 104.2

Therefore, the raw score is 104.2, which corresponds to choice B.

Question 20

A person has a score that is in the bottom 42% of the scores. What is the highest Z score this person could have? (Assume a normal distribution.)
A)-1.41
B)-)94
C)-)20
D)+)25

Accepted Answer

A Z score of -0.20 corresponds to the 42nd percentile in a standard normal distribution.

Quiz 4: Some Key Ingredients for Inferential Statistics: the Normal Curve, Sample Versus Population, and Probability

A person received a test score that was in the top 20% of everyone who has taken the test. The test scores are normally distributed. This person's Z score must be at least:

John attained a score of 65 on his stats exam. The mean for the class was a 70 with a SD of 10. What percentage of students scored below and above John?

The mean score on a creativity test is 20 and the standard deviation is 5. The distribution is normal. Using the percentage approximations for the normal curve, how many people would attain a score between 15 and 25?

What IQ score would a person need to be in the top 5% of the general population? Assume M = 100 and SD = 16.

The _____________ explains why many distributions tend to be close to normal in the real world.

On a normal curve, what percentage of scores fall between a Z score of 1.29 and a Z score of 1.49?

A person received a score of 4.78 on a test. This turned out to be a Z score of +1.5. What percentage are above this score? Assume a normal distribution.

What Z score would a person need to be in the 4% of his or her class on a particular test? Assume a normal distribution.

A person received a test score that is in the top 32% and the test scores follow a normal curve. This person's Z score must be at least:

If you were looking at a graph of a normal distribution, which of the following would best describe it?

Carrie attained a score of 650 on the verbal section of her SAT. The mean grade was a 500 with a standard deviation of 100. What percentage of test takers scored below and above Carrie?

The normal curve table shows percentages of scores:

Using the percentage approximations for the normal curve, what percentage of scores are between the mean and one standard deviation below the mean?

A particular nation has a human rights score of 41, which equals a Z score of 1.3. What is the percentage of nations above this score? (Assume a normal distribution.)

The mean score on a political attitude scale is 5 and the standard deviation is 2. The distribution is normal. Using the percentage approximations for the normal curve, how many people would get a score between 5 and 9?

What Z score would a person need to be in the top 5%? Assume a normal distribution.

If a person has an IQ of 130, approximately what percentage of people have higher IQs? Assume M = 100 and SD = 16.

Distributions observed in nature and research commonly approximate:

Jake's Z score for running ability is .60. What is Jake's raw score (assuming M =100 and SD = 7) .

A person has a score that is in the bottom 42% of the scores. What is the highest Z score this person could have? (Assume a normal distribution.)