Question 1119173
top 13% is z=+1.128
z=(x-mean)/sd=(x-79.7)/8.4=1.128
score=89.18 or 89
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bottom 56% is 44th percentile and z=-0.15
score is (x-79.7)=-.15*8.4
=78.4 or 78
range is [78, 89]
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Below top 44 and above the bottom 21
The top 44 are above z=+0.15 or a score of 80.96 or 81
Bottom 21% are at z of -0.81 or a score of 72.90 or 73
so range is [73, 81]

Top 79% are above the 21st percentile so any score below 73 is below the top 79%.  The bottom 9% are with z=-1.34 so -1.34=(x-79.7)/8.4
-11.26=x-79.7, so this score is 68.44 or 68
[68, 73]

Bottom 9% is <68