Question

nachelle earned a score of 725 on exam a that had a mean of 700 and a standard deviation of 50. she is about to take exam b that has a mean of 100 and a standard deviation of 20. how well must nachelle 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, $x = 725$, $\mu=700$, and $\sigma = 50$.
$z=\frac{725 - 700}{50}=\frac{25}{50}=0.5$

Step2: Use the z - score to find the score on Exam B

We know the z - score for Exam B should be the same as for Exam A (to do equivalently well). For Exam B, $\mu = 100$, $\sigma=20$, and $z = 0.5$. Rearranging the z - score formula $z=\frac{x - \mu}{\sigma}$ to solve for $x$ gives $x=z\sigma+\mu$.
$x=0.5\times20 + 100$
$x = 10+100=110$

Answer:

110