Answer
a. $547.6$
b. $183$
Work Step by Step
We have $\mu=400,\sigma=100$
a. The top 3% of students receive 500. What is the
minimum score you would need to receive this award?
$P(z1)=1-0.03=0.97, z1=1.4758$
$z1=\frac{X1-400}{100}=1.4758, X1=547.6$
b. The bottom 1.5% of students must go to summer
school. What is the minimum score you would need
to stay out of this group?
$P(z2)=0.015, z2=-2.17$
$z2=\frac{X2-400}{100}=-2.17, X2=183$
