Statistics

Eric has computed that it takes an average (mean) of 17 minutes with a standard deviation of 3 minutes to drive from home, park the car, and walk to his job. One day it took Eric 21 minutes to get to work. You would use the formula for transforming a raw score in a sample into a z-score to determine how many standard deviations the raw score represents. Since his "score" is 21, you would subtract the mean of 17 from 21 and divide that result (4) by the standard deviation of 3. The z-score of 1.33 tells you that Eric’s time to get to work is 1.33 standard deviations from the mean

Questions
Is the z value positive or negative? Explain why it should be positive or negative.
Another day, it took Eric only 12 minutes to get to work. Using the same formula, determine the z value. Is it positive or negative? Explain why it should be positive or negative.
On a different day, it took Eric 17 minutes to get from home to work. What is the z value? Why should you expect this result even before you did the calculation?
Based on your study of z-scores, explain the three uses of z-scores. How might they each relate to Eric's trip between home and work?
What is the relationship between z-scores and the standard normal curve?

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  1. Since Z = (score-mean)/SD, scores below the mean will have a negative value, and those above the mean will have a positive value.

    Since you did the calculation of the first Z score, you should be able to do the same for the other Z scores.

    For a normal distribution, the Z scores express raw scores in terms of SDs from the mean. The proportions cut off are the same for any normal distribution. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to your Z scores.

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