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.

Explanation:

Step1: Calculate z - score for Exam A

The formula for the z - score is $z=\frac{x - \mu}{\sigma}$, where $x$ is the score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Exam A, $x = 28$, $\mu=25$, and $\sigma = 4$.
So, $z=\frac{28 - 25}{4}=\frac{3}{4}=0.75$.

Step2: Use the same z - score for Exam B to find the required score

For Exam B, we know that $z = 0.75$, $\mu = 700$, and $\sigma=100$. We use the z - score formula and solve for $x$.
From $z=\frac{x-\mu}{\sigma}$, we can re - arrange it to $x=z\sigma+\mu$.
Substitute the values: $x=(0.75)\times100 + 700$.
First, calculate $(0.75)\times100 = 75$. Then, $x=75 + 700=775$.

Answer:

Daniel must score 775 on Exam B.