Question

luke earned a score of 850 on exam a that had a mean of 750 and a standard deviation of 50. he is about to take exam b that has a mean of 38 and a standard deviation of 5. how well must luke 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 the z - score for Exam A

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the raw score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Exam A, $x = 850$, $\mu=750$, and $\sigma = 50$.
$z_A=\frac{850 - 750}{50}=\frac{100}{50}=2$

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

We know that the z - score for Exam B should be the same as for Exam A ($z_B=z_A = 2$). For Exam B, $\mu = 38$ and $\sigma=5$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$ and solving for $x$, we get $x=z\sigma+\mu$.
Substitute $z = 2$, $\mu = 38$, and $\sigma = 5$ into the formula: $x=2\times5+38$.
$x = 10 + 38=48$

Answer:

48