2.5 z-Scores Practice

A normal distribution of scores has a standard deviation of 10. Find the z-score for a score of 60, where the mean of the sample data values is 40.

• 2

• 1.25

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CCSS.HSS.ID.A.4

A normal distribution of scores has a standard deviation of 10. Find the z-score for a score of 80, where the mean of the sample data values is 30.

• 2.33

• 5

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A normal distribution of scores has a standard deviation of 10. Find the z-score for a score of 20, where the mean of the sample data values is 50.

• 3

• 0.2

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CCSS.HSS.ID.A.4

IQ scores are normally distributed and have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.

What is the difference between Einstein’s IQ and the mean?

• 60

• 0.625

• 1.6

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CCSS.HSS.ID.A.4

IQ scores are normally distributed and have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.

Convert Einstein’s IQ score to a z-score.

• 0.27

• 3.75

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CCSS.HSS.ID.A.4

• unusual

• usual

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The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that the standard deviation is 84 pounds. How many standard deviations from the mean would a steer weighing 1000 pounds be?

• 1.81

• 0.55

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CCSS.HSS.ID.A.4

One of the authors has an adopted grandson whose birth family members are very short. After examining him at his 2-year checkup, the boy’s pediatrician said that the z-score for his height relative to American 2-year-olds was -1.88. Choose the sentence that explains what this means.

• His height is 1.88 standard deviations above the mean height of American 2-year-olds.

• His height is 1.88 standard deviations below the mean height of American 2-year-olds.

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The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Greg’s z -score was -2. How many points did he score?

• 55

• 45

• 65

• 75

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CCSS.HSS.ID.A.4

The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that the standard deviation is 84 pounds.

What’s the actual weight of an animal whose z -score is -1.5?

• 1026 lb

• 1278 lb

• 982 lb

• 1102 lb

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CCSS.HSS.ID.A.4