Question

boubacar earned a score of 270 on exam a that had a mean of 250 and a standard deviation of 20. he is about to take exam b that has a mean of 700 and a standard deviation of 25. how well must boubacar 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, $x = 270$, $\mu = 250$, $\sigma = 20$. So, $z = \frac{270 - 250}{20} = \frac{20}{20} = 1$.

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

For Exam B, we know the z-score should be the same (1) to do equivalently well. The mean $\mu = 700$, standard deviation $\sigma = 25$. Using the z-score formula rearranged to solve for $x$: $x = \mu + z\sigma$. Substituting the values, $x = 700 + 1\times25 = 725$.

Answer:

725