Answer
$X_A=76.45$
$X_B=68.42$
$X_C=51.58$
$X_D=43.55$
Work Step by Step
As shown in the figure,
given $\mu=60,\sigma=10$ and the probability to the left of each boundary
$P(A)=1-0.05=0.95,P(B)=P(A)-0.15=0.80$,
$P(C)=P(B)-0.6=0.2, P(D)=P(C)-0.15=0.05$
Use Table E to get the z-values for each probability:
$z_A=1.645,z_B=0.842,z_C=-0.842,z_D=-1.645$
Using formula $z=\frac{X-\mu}{\sigma}$, we can get $X=\mu+z\sigma$ for each
$X_A=60+1.645\times10=76.45$
$X_B=60+0.842\times10=68.42$
$X_C=60-0.842\times10=51.58$
$X_D=60-1.645\times10=43.55$
The above numbers give the scores that divide the
distribution into those categories.
