Question

emma earned a score of 510 on exam a that had a mean of 550 and a standard deviation of 100. she is about to take exam b that has a mean of 79 and a standard deviation of 25. how well must emma 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 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, $x = 510$, $\mu = 550$, $\sigma = 100$. So, $z_{A} = \frac{510 - 550}{100} = \frac{-40}{100} = -0.4$.

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

For Exam B, we know the z-score should be the same as Exam A (to do equivalently well), so $z_{B} = z_{A} = -0.4$. The formula for $x$ from z-score is $x = \mu + z\sigma$. For Exam B, $\mu = 79$, $\sigma = 25$, $z = -0.4$. So, $x = 79 + (-0.4)\times25 = 79 - 10 = 69$.

Answer:

69