Question

carter earned a score of 43 on exam a that had a mean of 35 and a standard deviation of 4. he is about to take exam b that has a mean of 200 and a standard deviation of 20. how well must carter 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 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, $x = 43$, $\mu=35$, $\sigma = 4$.
So, $z_{A}=\frac{43 - 35}{4}=\frac{8}{4}=2$.

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

We know that for Exam B, $z = z_{A}=2$, $\mu = 200$, $\sigma=20$.
Using the z - score formula $z=\frac{x - \mu}{\sigma}$, we can solve for $x$.
Rearranging the formula gives $x=z\sigma+\mu$.
Substituting the values: $x = 2\times20+200$.
First, calculate $2\times20 = 40$.
Then, $x=40 + 200=240$.

Answer:

240