Chapter 5 Quiz Review

Which of the following shows a z-score, corresponding to one standard deviation below the mean?

• 1

• 0

• -1

• -1.5

Answer explanation

One of the primary purposes of a z-score is to describe the exact location of a score within a distribution. The Z-scores sign will tell us if it's above or below the mean and the number tells us the magnitude. Since the problem says our score is "one standard deviation below the mean," we know the corresponding Z-score must be -1.

For a population with μ = 20 and σ = 4, find the Z-score for a raw score of X = 18.

• z = 0.50

• z = -0.50

• z = 0

• z = -1

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CCSS.HSS.ID.A.4

For a population with μ = 60 and σ = 20, what does the X value have to be if we obtain a Z-score of z = 2.00?

• X = 120

• X = 100

• X = 55

• X = 98

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CCSS.HSS.ID.A.4

In a distribution with σ = 12, X = 56, and z = -0.50, what must the mean (μ) be?

• μ = 62

• μ =60

• μ = 64

• μ = 66

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CCSS.HSS.ID.A.4

A normal-shaped distribution with μ = 40 and σ = 8 is transformed into z-scores. The resulting distribution of z-scores will have a mean of ___ and a standard deviation of ___.

• 1; 0

• 1; 1

• 1; -1

• 0; 1

Answer explanation

When any distribution is transformed into z-scores, the transformed distribution will always have μ = 0 and σ = 1.

A sample has a mean of M = 30 and a standard deviation of s = 2. If given a raw score of X = 36, would this be considered a central or extreme score?

• Extreme (z = 3.00)

• Central (z = 0.75)

• Extreme (z = -3.00)

• Central (z = 3.00)

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CCSS.HSS.ID.A.4

The locations identified by z-scores are the same for all distributions, no matter what mean or standard deviation a distribution might have.

• True

• False

If we want a greater value for our z-score we must:

• Decrease the numerator

• Increase the denominator

• Increase the numerator

• You cannot increase the value of z.

Answer explanation

*Hint: These types of questions are Dr. Story's favorite so make sure you remember!* If you ever want to increase a score you're solving for, always increase the numerator to yield a greater value.

The skewness and kurtosis values change when you standardize a distribution.

• True

• False

Answer explanation

This is false! The shape and spread of your distribution remain the same, leaving your skewness and kurtosis values unchanged.

What percent of scores fall within one standard deviation of the mean?

• 66%

• 70%

• 68%

• 69%

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CCSS.HSS.ID.A.4