Question

morgan earned a score of 670 on exam a that had a mean of 650 and a standard deviation of 20. she is about to take exam b that has a mean of 72 and a standard deviation of 10. how well must morgan score on exam b in order to do equivalently well as she did on exam a? assume that scores on each exam are normally distributed.

Explanation:

Step1: Calculate z-score for Exam A

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Exam A, $x = 670$, $\mu=650$, $\sigma = 20$.
So, $z_{A}=\frac{670 - 650}{20}=\frac{20}{20}=1$.

Step2: Use z - score to find score for Exam B

For Exam B, we know that $z_{B}=z_{A}=1$ (since she wants to do equivalently well), $\mu_{B}=72$, $\sigma_{B}=10$. Using the z - score formula $z=\frac{x - \mu}{\sigma}$, we can solve for $x$ (the score on Exam B).
Rearranging the formula gives $x=\mu + z\sigma$.
Substitute $\mu = 72$, $z = 1$, $\sigma=10$ into the formula: $x=72+1\times10 = 82$.

Answer:

Morgan must score 82 on Exam B.