SOLUTION: Looking at IQ-Tests, let us assume a standard IQ design that is µ=100 and σ=15 to answer the question. From what score to what other score accounts for the middle 50 percent?

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Question 873841: Looking at IQ-Tests, let us assume a standard IQ design that is µ=100 and σ=15 to answer the question.
From what score to what other score accounts for the middle 50 percent? What actual score corresponds to the top 80th percentile?
I believe this has something to do with converting to a z-score, but I am not sure where to start.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Looking at IQ-Tests, let us assume a standard IQ design that is µ=100 and σ=15 to answer the question.
From what score to what other score accounts for the middle 50 percent?
For the lower score, enter the following formula in Excel:
=100+15*NORMSINV(.25)
The result is 89.8827
For the upper score, enter the following formula in Excel:
=100-15*NORMSINV(.25)
The result is 110.1173
Therefore, the middle score is from highlight%2889.8827%29 to highlight%28110.1173%29

What actual score corresponds to the top 80th percentile?
To get the 80th percentile, enter the following formula in Excel:
=15*NORMSINV(0.8)+100
The result is highlight%28112.6243%29