Question

anna earned a score of 725 on exam a that had a mean of 750 and a standard deviation of 25. she is about to take exam b that has a mean of 32 and a standard deviation of 4. how well must anna 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 formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Exam A, $x = 725$, $\mu=750$, and $\sigma = 25$.
So, $z_{A}=\frac{725 - 750}{25}=\frac{- 25}{25}=- 1$.

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

For Exam B, we know that $z = z_{A}=-1$, $\mu = 32$, and $\sigma = 4$. We use the z - score formula $z=\frac{x - \mu}{\sigma}$ and solve for $x$.
Rearranging the formula gives $x=\mu+z\sigma$.
Substitute the values: $x = 32+(-1)\times4=32 - 4 = 28$.

Answer:

28