Question

david earned a score of 41 on exam a that had a mean of 51 and a standard deviation of 10. he is about to take exam b that has a mean of 300 and a standard deviation of 40. how well must david 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 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, $x = 41$, $\mu=51$, $\sigma = 10$.
So, $z=\frac{41 - 51}{10}=\frac{- 10}{10}=- 1$.

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

For Exam B, we know that $z=-1$, $\mu = 300$, $\sigma=40$.
We use the z - score formula $z=\frac{x-\mu}{\sigma}$ and solve for $x$.
Rearranging the formula for $x$ gives $x=\mu+z\times\sigma$.
Substitute the values: $x = 300+(-1)\times40=300 - 40 = 260$.

Answer:

260