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

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 average waist size for teenage males is 29 inches with a standard deviation of 2 inches. 
If waist sizes are normally distributed, determine the z-score of a teenage male with a 33 inch waist.  

• 2
• 1
• -2
• -1

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CCSS.HSS.ID.A.4

μ = 70 , σ = 8 , X = 50 . Find z score

• 2.5
• -2.5
• 5.2
• -5.2

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CCSS.HSS.ID.A.4

Brian scored an 80% on a Chemistry Exam. The average on the exam was a 68%, with a standard deviation of 5%. What is Brian's z-score?

• 2.4

• -2.4

• 1.1

• -1.1

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CCSS.HSS.ID.A.4

The mean temperature in Glens Falls for the month of February is 23 degrees with a standard deviation of 4.2 degrees. What is the z-score for a temperature of 17 degrees?

• 1

• 1.43

• -1.43

• 11.5

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CCSS.HSS.ID.A.4

1) What will be the miles per gallon for a Toyota Camry when the average mpg is 23, it has a z value of 1.5 and a standard deviation of 2?

• 25

• 20

• 26

• 68

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CCSS.HSS.ID.A.4

A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?

• 82
• 88
• 100
• 118

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CCSS.HSS.ID.A.4

Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches.  The z score corresponding to a woman with a height is 2.56. How tall is the woman?

• 24.42 in
• 70 in
• 28in
• 68.6in

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CCSS.HSS.ID.A.4

On the Wechsler IQ test, the average IQ is 100 with a standard deviation of 15. Genius IQ would be an IQ above the average range. Low incidents intellectual disability would correspond to a z-score less then -3. What would the IQ be less than?

• 100

• -55

• 70

• 55

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CCSS.HSS.ID.A.4