Please help, very lost
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.
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. It is simple what happens when you subtract 21 from 21.
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?
To determine the z value for Eric's commute time of 12 minutes, we can use the same formula as before. We subtract the mean of 17 minutes from the raw score of 12 minutes and divide that result (-5) by the standard deviation of 3 minutes.
The z value is -5/3, which equals -1.67. This z value is negative because the raw score (12 minutes) is below the mean (17 minutes). In other words, Eric's commute time of 12 minutes is 1.67 standard deviations below the mean.
For Eric's commute time of 17 minutes, the z value can be calculated as (17 - 17) / 3, which equals 0. Since the raw score is equal to the mean, there is no deviation from the mean, and hence the z value is 0.
Before even performing the calculation, we would expect a z value of 0 for Eric's commute time of 17 minutes. This is because the mean represents the average value, and when the raw score is equal to the mean, there is no deviation or difference from that average. Therefore, we would not expect any positive or negative deviation, hence a z value of 0.