Answer
A: The top 6%: $x\gt76.36$
B: The next 14%: $70.72\lt x\leq76.36$
C: The middle 60%: $57.28\lt x\leq70.72$
D: $51.64\lt x\leq57.28$
Fail: The bottom 6%: $x\leq51.64$
Work Step by Step
A: The top 6% (94th percentile)
B: The next 14% (from 80th percentile to 94th percentile)
C: The middle 60%: (from 20th percentile to 80th percentile)
Fail: The bottom 6%: (up to 6th percentile)
D: The rest: (from 6th percentile to 20th percentile)
The z-score which gives an area of 0.94 to the left is $\frac{1.54+1.55}{2}=1.545$
The z-score which gives an area of 0.80 to the left is 0.84
The z-score which gives an area of 0.20 to the left is -0.84
The z-score which gives an area of 0.06 to the left is $\frac{-1.54+(-1.55)}{2}=-1.545$
Let $x$ be the exam scores:
$z=\frac{x-μ}{σ}$, that is:
$x=zσ+μ$
For $z=1.545$: $x=1.545\times8+64=76.36$
For $z=0.80$: $x=0.84\times8+64=70.72$
For $z=0.20$: $x=-0.84\times8+64=57.28$
For $z=0.06$: $x=-1.545\times8+64=51.64$
