Question

normal distribution - equivalent scores
score: 0/5 penalty: 1 off
question
luke earned a score of 32 on exam a that had a mean of 50 and a standard deviation of 10. he is about to take exam b that has a mean of 200 and a standard deviation of 25. 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.
answer attempt 1 out of 2

Explanation:

Step1: Calculate the 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, $x = 32$, $\mu=50$, and $\sigma = 10$. So, $z=\frac{32 - 50}{10}=\frac{-18}{10}=-1.8$.

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

We know that for Exam B, $\mu = 200$, $\sigma=25$, and we use the z - score formula $z=\frac{x-\mu}{\sigma}$ to find $x$. Rearranging the formula for $x$ gives $x=z\sigma+\mu$. Substituting $z=-1.8$, $\mu = 200$, and $\sigma = 25$ into the formula, we get $x=-1.8\times25 + 200$. First, calculate $-1.8\times25=-45$. Then, $x=-45 + 200=155$.

Answer:

155