Question

emily earned a score of 550 on exam a that had a mean of 450 and a standard deviation of 100. she is about to take exam b that has a mean of 350 and a standard deviation of 50. how well must emily 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, $x = 550$, $\mu=450$, and $\sigma = 100$. So, $z_A=\frac{550 - 450}{100}$.
$z_A=\frac{100}{100}=1$

Step2: Use the z - score for Exam B

We want the z - score for Exam B, $z_B$, to be equal to $z_A$. For Exam B, $\mu = 350$, $\sigma=50$, and $z_B = 1$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$ and solving for $x$ (the score on Exam B), we get $x=z_B\sigma+\mu$. Substitute $z_B = 1$, $\sigma = 50$, and $\mu = 350$ into the formula.
$x=1\times50 + 350$
$x = 400$

Answer:

400