Question

question
tallulah earned a score of 470 on exam a that had a mean of 500 and a standard deviation of 20. she is about to take exam b that has a mean of 300 and a standard deviation of 40. how well must tallulah 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 formula for the z - score 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, $x = 470$, $\mu=500$, and $\sigma = 20$.
So, $z_{A}=\frac{470 - 500}{20}=\frac{- 30}{20}=-1.5$

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

We want the same z - score for Exam B. For Exam B, $\mu_{B}=300$, $\sigma_{B}=40$, and $z = z_{A}=-1.5$. We use the z - score formula $z=\frac{x-\mu}{\sigma}$ and solve for $x$ (the score on Exam B).
Rearranging the formula gives $x=\mu+z\sigma$.
Substitute $\mu = 300$, $z=-1.5$, and $\sigma = 40$ into the formula:
$x=300+(-1.5)\times40=300 - 60 = 240$

Answer:

240