AP Statistics : How to find z-scores for a data set

Study concepts, example questions & explanations for AP Statistics

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Example Questions

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Example Question #51 : Data

The observed times (in minutes) it takes a swimmer to complete a race are normally distributed. The z-score for her swimming time this week is . Which one of the following statements is correct interpretation of this z-score?

Possible Answers:

This week her time was two standard deviations lower than her average time. 

This week her time was two minutes lower than her best time ever. 

This week her time was two minutes lowere than her time last week.

This week her time was two minutes lower than her average time. 

This week her time was two standard deviations lower than her time last week. 

Correct answer:

This week her time was two standard deviations lower than her average time. 

Explanation:

The z-score =  and a negative z-score indicates that the x-value is below the average. The value of the score represents the difference between the x-value and the mean in terms of the number of standard deviations. 

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