Interpreting z-scores

What is the purpose of z-scores?

• to describe the exact location of a score within a distribution

• to find the mean of the distribution

• to describe the shape of the distribution

• to find the standard deviation of the distribution

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CCSS.HSS.ID.A.4

z-scores are the standardized scores for X values

• True

• False

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CCSS.HSS.ID.A.4

What is the formula to find the z-score for population?

• z=X-M

• z=σ-M/μ

• ^z/M=μ

• z=X-μ/σ

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CCSS.HSS.ID.A.4

The sign of the z-score indicates whether the location is above(positive) or below(negative) the mean.

• True

• False

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CCSS.HSS.ID.A.4

Find the z-score value corresponding if the location is below the mean by 2 standard deviations

• +2.00

• -2.00

• +1.25

• -1.00

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CCSS.HSS.ID.A.4

Find the z-scores value corresponding if the location is above the mean by 1/2 standard deviations

• -0.50

• +1.00

• +0.50

• -1.00

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CCSS.HSS.ID.A.4

A data set has a mean of 290 and a standard deviation of 20. Calculate the z-score for 265.

• $z=250.5$

• $z=1.25$

• $z=-1.02$

• $z=-1.25$

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CCSS.HSS.ID.A.4

A data set has a mean of 20 and a standard deviation of 3. Calculate the z-score for 23.

•  $z=-1$  

•  $z=16.33$  

•  $z=1$  

•  $z=3$  

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CCSS.HSS.ID.A.4

A data set has a mean of 300 and a standard deviation of 40. What value would have a z-score of  $z=-2$  ?

• 298

• 296

• 220

• 380

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CCSS.HSS.ID.A.4

Steve took his math test and scored an 88. If the class average was a 78 with a standard deviation of 5, what percent of students earned a grade that was higher than Steve's grade?

• 97.5%

• 93%

• 5%

• 2.5%

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CCSS.HSS.ID.A.4