# Z-scores and Extreme Scores

Please explain how I set up and solve this problem:

For each of the populations would a score of x= 50 be considered a central score (near the middle of the distribution) or an extreme score (far out of the tail of the distribution ) is this set up x-u/o?

u=45 o= 10

u=45 o= 2

u= 90 o= 20

u= 60 o=20

If i have a problem that is a distribution with a mean of u=38 and a standard deviation of o=5 is transformed into a standardized distribution with u= 50 and o= 10. Now i need to find the new standardized score for each value from the original population. I have no clue how to set this up and solve it. Please explain in steps if possible.

original x= 39 transformed x=____

original x= 43 transformed x=____

original x= 35 transformed x=____

original x= 28 transformed x=____.

https://brainmass.com/statistics/statistical-theory/zscores-extreme-scores-583996

#### Solution Preview

1. An extreme score happens when z value is above 2 or below -2.

So if x=50, z=(50-45)/10=0.5 (central score)

if x=50, z=(45-45)/2=0 ...

#### Solution Summary

The solution gives detailed steps on determining central score and extreme score and transforming between two normal random variables. All steps are shown with brief explanations.

Normal probability z-scores

If a student had a z-score of 1, what would be the raw score (rating)?

If a student had a z-score of 1, what percentage of the participants would be

expected to rate the product higher than he/she did?

If a student gave a rating of 75, what would be the z-score?

What is the probability that a rating is below 51.03?

What is the probability that a rating is higher than 80?

What percentage of participants would be expected to rate the product lower than 75?

What is the probability that a rating falls between 25 and 65?

What is the probability that a rating falls between 75 and 80?

If the z-score is 2, what is the rating?

If the rating is 21, what is the z-score?

What is the probability of observing a rating lower than 20 or higher than 80?

4. What if one participant gave a particularly odd (extreme) rating? How extreme would it have to be for us to suspect that it should be discounted (i.e., the participant was rating a different product or was trying to ruin our data or wasn't really paying attention to the task)?

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