Question 1161078
the 97.5th percentile is 45.68 or 46 points
calculator 2 VARS 3 invnorm (.975,30,8)

99.85 percentile is 2.967 sd
97.5 percentile is 1.96 sd

z=(x-mean)/sd
so 2.967=(x-mean)/sd
and -1.96=(x-mean)/sd
2.97 sd=26-mean 
-1.96 sd=6-mean
1.96 sd=-6+mean
4.93 sd=20
sd=4.056 or 4.06 points

(26-mean)=4.06*2.967=12.05
mean=13.95 points

check
26-13.95 divided by 4.06=12.05/4.06 or 2.97 points standard deviation.
and
-7.95/4.06=-1.96 sd 

can check using normalcdf (6,26,13.95,4.06), which should be everything but 0.15% on the left and 2.5% on the right or 100-2.65=97.35%, and it is 97.34%