Question

normal distribution - equivalent scores
score: 2/5 penalty: 1 off
question
daniel earned a score of 28 on exam a that had a mean of 25 and a standard deviation of 4. he is about to take exam b that has a mean of 700 and a standard deviation of 100. how well must daniel 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, $x = 28$, $\mu=25$, $\sigma = 4$. So $z=\frac{28 - 25}{4}=\frac{3}{4}=0.75$.

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

We know the z - score for Exam B should be the same as for Exam A. For Exam B, $\mu = 700$, $\sigma=100$, and $z = 0.75$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$ and solving for $x$, we get $x=z\sigma+\mu$. Substitute $z = 0.75$, $\sigma = 100$, and $\mu = 700$ into the formula: $x=0.75\times100 + 700=700 + 75=775$.

Answer:

775