Question 1

Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?
A)when the population mean is much less than 5
B)when the population mean is much greater than 5
C)when the population standard deviation is much less than 5
D)when the population standard deviation is much greater than 5

Accepted Answer

A score 5 points above the mean is considered relatively close to the mean when the population standard deviation is much greater than 5, indicating that the data is spread out and 5 points is a small deviation.

Question 2

Last week Sarah had exams in Math and in Spanish.On the Math exam, the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45.On the Spanish exam, the mean was µ = 60 with σ = 8 and Sarah had a score of X = 68.For which class should Sara expect the better grade?
A)Math
B)Spanish
C)The grades should be the same because the two exam scores are in the same location.
D)There is not enough information to determine which is the better grade.

Accepted Answer

The answer of Last week Sarah had exams in Math...

Question 3

Last week Sarah had exams in Math and in Spanish.On the Math exam, the mean was µ = 30 with σ = 5, and Sarah had a score of X = 45.On the Spanish exam, the mean was µ = 60 with σ = 8 and Sarah had a score of X = 68.For which class should Sara expect the better grade?
A)Math
B)Spanish
C)The grades should be the same because the two exam scores are in the same location.
D)There is not enough information to determine which is the better grade.

Accepted Answer

Sarah's score in Math is 3 standard deviations above the mean ((45-30)/5 = 3), while her score in Spanish is 1 standard deviation above the mean ((68-60)/8 = 1). Therefore, she should expect a better grade in Math.

Question 4

For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00.What are the values for the sample mean and standard deviation?
A)M = 35 and s = 10
B)M = 30 and s = 15
C)M = 35 and s = 15
D)M = 30 and s = 10

Accepted Answer

The answer of For a sample of n = 30...

Question 5

A population with µ = 85 and σ = 12 is transformed into z-scores.After the transformation, what is the standard deviation for the population of z-scores?
A)σ = 12
B)σ = 1.00
C)σ = 0
D)cannot be determined from the information given

Accepted Answer

The standard deviation of a population of z-scores is always 1.00, regardless of the original population's standard deviation.

Question 6

A sample has M = 72 and s = 4.In this sample, what is the X value corresponding to z = -2.00?
A)X = 70
B)X = 68
C)X = 64
D)X = 60

Accepted Answer

We can use the formula: z = (X - M) / s
Rearranging the formula, we get: X = z * s + M
Substituting the given values, we get: X = (-2.00) * 4 + 72 = 64
Therefore, the X value corresponding to z = -2.00 is 64, so the best choice is C.

Question 7

For any distribution, what is the z-score corresponding to the mean?
A)0
B)1
C)N
D)cannot be determined from the information given

Accepted Answer

The z-score is a measure of how many standard deviations a data point is away from the mean. The mean is the average of all the data points in a distribution. By definition, the mean has a z-score of 0.

Question 8

For a sample with M = 80, a score of X = 88 corresponds to z = 2.00.What is the sample standard deviation?
A)2
B)4
C)8
D)16

Accepted Answer

The formula for calculating a z-score is z = (X - M) / SD, where X is the score, M is the mean, and SD is the standard deviation. Plugging in the given values, 2 = (88 - 80) / SD. Solving for SD, we get SD = 8 / 2 = 4.

Question 9

A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8.In this sample, what is the z-score corresponding to X = 57?
A)z = 12/20 = 0.60
B)z = 1.00
C)z = 1.50
D)z = 2.00

Accepted Answer

To calculate the z-score, we use the formula z = (X - M) / s. Plugging in the values, we get z = (57 - 45) / 8 = 1.5. Therefore, the z-score corresponding to X = 57 is 1.50.

Question 10

Using z?scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10.After the standardization, one individual has a score of X = 55.What was this individual's score in the original distribution?
A)X = 40
B)X = 42
C)X = 43
D)cannot be determined with the information given

Accepted Answer

The z-score for X = 55 is (55 - 50) / 10 = 0.5. The corresponding score in the original distribution is 0.5 * 6 + 37 = 43.

Question 11

A sample with M = 85 and s = 12 is transformed into z-scores.After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?
A)M = 85 and s = 12
B)M = 0 and s = 12
C)M = 85 and s = 1
D)M = 0 and s = 1

Accepted Answer

When transforming a sample into z-scores, the mean is always transformed into 0 and the standard deviation is always transformed into 1. Therefore, the answer is D, with a mean (M) of 0 and a standard deviation (s) of 1.

Question 12

A distribution with µ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10.In the new, standardized distribution your score is X = 45.What was your score in the original distribution?
A)X = 30
B)X = 31
C)X = 39
D)X = 45

Accepted Answer

To standardize a score from an original distribution to a new distribution, you can use the formula: $Z = \frac{(X - \mu)}{\sigma}$, where $X$ is the score in the original distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation. In this case, we are given the standardized score (45 in the new distribution with $\mu = 50$ and $\sigma = 10$), and we need to find the original score in the distribution with $\mu = 35$ and $\sigma = 8$.First, find the Z-score in the new distribution: $Z = \frac{(45 - 50)}{10} = -0.5$.Then, apply this Z-score to the original distribution to find the original score: $X = Z\sigma + \mu = -0.5 \times 8 + 35 = 31$.Therefore, the original score was 31.

Question 13

If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ___ and a standard deviation of ___.
A)0 and 1
B)60 and 1
C)0 and 8
D)60 and 8 (unchanged)

Accepted Answer

When a distribution is transformed into z-scores, the mean becomes 0 and the standard deviation becomes 1.

Question 14

Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?
A)when the population mean is much larger than 15
B)when the population standard deviation is much larger than 15
C)when the population mean is much smaller than 15
D)when the population standard deviation is much smaller than 15

Accepted Answer

A score 15 points above the mean is considered extreme when the population standard deviation is much smaller than 15, as it indicates that the score is far from the mean relative to the spread of the data.

Question 15

For any distribution, what is the z-score corresponding to the median?
A)0
B)1
C)N
D)cannot be determined from the information given

Accepted Answer

The z-score corresponding to the median cannot be determined without knowing the specific distribution, as the median is not necessarily the mean in non-symmetrical distributions.

Question 16

For a sample with s = 12, a score of X = 73 corresponds to z = -1.00.What is the sample mean?
A)M = 61
B)M = 67
C)M = 79
D)M = 85

Accepted Answer

The answer of For a sample with s = 12,...

Question 17

In a sample with M = 40 and s = 8, what is the z-score corresponding to X = 38.
A)z = -0.25
B)z = -0.50
C)z = 0.25
D)z = 0.50

Accepted Answer

The answer of In a sample with M = 40...

Question 18

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10.When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution?
A)X = 53
B)X = 55
C)X = 58
D)X = 61

Accepted Answer

To standardize a score, we use the formula z = (X - µ) / σ. 
For the original distribution with µ = 55 and σ = 6, we plug in X = 58 and solve for z: 
z = (58 - 55) / 6 = 0.5 
Now we want to find the corresponding X value from the standardized distribution with µ = 50 and σ = 10. We use the formula X = µ + zσ and plug in the values we know: 
X = 50 + 0.5(10) = 55 
Therefore, a score of X = 58 from the original distribution will correspond to a standardized score (z-score) of 0.5 and a new X value of 55 from the standardized distribution. Choice B is the correct answer.

Question 19

A sample of n = 20 scores is transformed into z-scores.What is the mean for the set of 20 z-scores?
A)0
B)1
C)10
D)cannot be determined without more information

Accepted Answer

The mean of a set of z-scores is always 0, regardless of the sample size.

Question 20

In N = 25 games last season, the college basketball team averaged µ = 76 points with a standard deviation of σ = 6.In their final game of the season, the team scored 89 points.Based on this information, the number of points scored in the final game was _____.
A)a little above average
B)far above average
C)above average, but it is impossible to describe how much above average
D)There is not enough information to compare last year with the average.

Accepted Answer

The team's average score for the season was 76 points with a standard deviation of 6. Therefore, a score of 89 points in the final game is considered a significant increase and is far above the average.

Quiz 5: Z-Scores

Under what circumstances is a score that is located 5 points above the mean a central value, relatively close to the mean?

Last week Sarah had exams in Math and in Spanish.On the Math exam, the mean was µ = 40 with σ = 5 and Sarah had a score of X = 45.On the Spanish exam, the mean was µ = 60 with σ = 8 and Sarah had a score of X = 68.For which class should Sara expect the better grade?

Last week Sarah had exams in Math and in Spanish.On the Math exam, the mean was µ = 30 with σ = 5, and Sarah had a score of X = 45.On the Spanish exam, the mean was µ = 60 with σ = 8 and Sarah had a score of X = 68.For which class should Sara expect the better grade?

For a sample of n = 30 scores, X = 45 corresponds to z = 1.50 and X = 40 corresponds to z = +1.00.What are the values for the sample mean and standard deviation?

A population with µ = 85 and σ = 12 is transformed into z-scores.After the transformation, what is the standard deviation for the population of z-scores?

A sample has M = 72 and s = 4.In this sample, what is the X value corresponding to z = -2.00?

For any distribution, what is the z-score corresponding to the mean?

For a sample with M = 80, a score of X = 88 corresponds to z = 2.00.What is the sample standard deviation?

A sample of n = 20 scores has a mean of M = 45 and a standard deviation of s = 8.In this sample, what is the z-score corresponding to X = 57?

Using z?scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10.After the standardization, one individual has a score of X = 55.What was this individual's score in the original distribution?

A sample with M = 85 and s = 12 is transformed into z-scores.After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

A distribution with µ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10.In the new, standardized distribution your score is X = 45.What was your score in the original distribution?

If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of _ and a standard deviation of _.

Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?

For any distribution, what is the z-score corresponding to the median?

For a sample with s = 12, a score of X = 73 corresponds to z = -1.00.What is the sample mean?

In a sample with M = 40 and s = 8, what is the z-score corresponding to X = 38.

A distribution with µ = 55 and σ = 6 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10.When the distribution is standardized, what value will be obtained for a score of X = 58 from the original distribution?

A sample of n = 20 scores is transformed into z-scores.What is the mean for the set of 20 z-scores?

In N = 25 games last season, the college basketball team averaged µ = 76 points with a standard deviation of σ = 6.In their final game of the season, the team scored 89 points.Based on this information, the number of points scored in the final game was _____.