Question

question
mamadou earned a score of 260 on exam a that had a mean of 350 and a standard deviation of 100. he is about to take exam b that has a mean of 700 and a standard deviation of 40. how well must mamadou 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, $x = 260$, $\mu=350$, $\sigma = 100$.
So, $z_{A}=\frac{260 - 350}{100}=\frac{- 90}{100}=-0.9$.

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

For Exam B, we know that the z - score should be the same as that of Exam A (to do equivalently well), so $z_{B}=z_{A}=-0.9$. The formula for the score $x$ from the z - score is $x=\mu + z\sigma$. For Exam B, $\mu = 700$, $\sigma=40$, and $z=-0.9$.
So, $x=700+(-0.9)\times40=700 - 36 = 664$.

Answer:

664