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Z-scores and Extreme Scores

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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=____.

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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.

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