Question

gavin earned a score of 330 on exam a that had a mean of 450 and a standard deviation of 40. he is about to take exam b that has a mean of 150 and a standard deviation of 25. how well must gavin score on exam b in order to do equivalently well as he 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, $x = 330$, $\mu=450$, and $\sigma = 40$.
$z=\frac{330 - 450}{40}=\frac{- 120}{40}=-3$

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

We know that the z - score for Exam B should be the same as the z - score for Exam A. For Exam B, $\mu = 150$, $\sigma=25$, and $z=-3$. Using the z - score formula $z=\frac{x - \mu}{\sigma}$ and solving for $x$, we get $x=z\sigma+\mu$.
$x=-3\times25 + 150$
$x=-75 + 150$
$x = 75$

Answer:

75