# 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.