Answer
Julie performed better on the exam
Work Step by Step
1st:
Derrick: $z=\frac{y-\mu}{\rho}=\frac{80-65}{10}=1.5$
Julie: $z=\frac{y-\mu}{\rho}=\frac{70-65}{10}=0.5$
2nd:
Derrick: $z=\frac{y-\mu}{\rho}=\frac{80-80}{5}=0$
Julie: $z=\frac{y-\mu}{\rho}=\frac{90-80}{5}=2.0$
Total:
Derrick: $1.5+0=1.5$
Julie: $0.5+2.0=2.5$
So Julie performed better on the exam whose standard deviation was smaller giving her a greater standard deviation.
