Stats Z-scores

A z-score of z = -2.00 indicates a position

below the mean by 2 times the standard deviation

For a population with a standard deviation of σ = 5, a score that is located 10 points below the mean would have a z-score of ________.

-2

For a population with μ = 60 and σ = 8, the z-score corresponding to X = 62 is z = ________.

0.25

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

0; 1

In a population with μ = 60, a score of X = 58 corresponds to a z-score of z = -0.50. What is the population standard deviation?

4

A set of score has a mean of μ = 63 and a standard deviation of σ = 8. If these scores are standardized so that the new distribution has μ = 50 and σ = 10, what new value would be obtained for a score of X = 59 from the original distribution?

45

A population with μ = 37 and σ = 6 is standardized to create a new distribution with μ = 100 and σ = 10. In this transformation, a score of X = 40 from the original distribution will be transformed into a score of X = 110.

False

For a population with μ = 100 and σ = 20, the z-score corresponding to X = 90 is z = +0.50.

False

For a population with μ = 60, a score of X = 65 corresponds to z = 0.50. The standard deviation for the population is σ = 5.

False

One advantage of transforming X values into z-scores is that the transformation always creates a normal distribution.

False

Last week, Bob had a score of X = 45 on a mathematics exam and a score of X = 61 on an English exam. If the math exam scores had a mean of μ = 40 with σ = 5, and the English exam scores had a mean of μ = 51 with σ = 10, for which exam should Bob expect the better grade in comparison to his classmates?

The two exam scores are in equivalent locations so Bob should expect the same grade in both classes.

A population with μ = 100 and σ = 20 is transformed into z-scores. The resulting distribution of z-scores will have a mean of zero.

True

A z-score of z = +2.00 indicates a position located exactly two standard deviations above the mean.

True

Any score with a value less than the population mean will have a negative z-score.

True

For a population with μ = 100 and σ = 20, the X value corresponding to z = 1.50 is X = 130.

True

For a population with σ = 4, a score of X = 40 corresponds to z = -2.00. The mean for the population is μ = 48.

True

Transforming an entire distribution of scores into z-scores will not change the shape of the distribution.

True

For a population with μ = 100 and σ = 10, the score corresponding to z = 1.50 is X = ________.

X = 115

Last week, Bob had a score of X = 45 on a mathematics exam and a score of X = 61 on an English exam. For which exam should Bob expect the better grade?

cannot answer without additional information

For a population with a mean of μ = 70, a score that is located 10 points below the mean would have a z-score of ________.

cannot answer without knowing the standard deviation

Under what circumstances would a score that is located 5 points above the mean be considered an extreme score?

when the population standard deviation is much less than 5

In a population with σ = 8, a score of X = 44 corresponds to a z-score of z = -.50. What is the population mean?

μ = 48

You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam?

μ = 60 and σ = 5

A population has μ = 50. What value of σ would make X = 55 an extreme score in this population?

σ = 1

On an exam with μ = 52, you have a score of X = 48. Which value for the standard deviation would give you a higher position in the class distribution?

σ = 4