Question

normal distribution - equivalent scores
score: 1/5 penalty: 1 off
question
mariana earned a score of 338 on exam a that had a mean of 350 and a standard deviation of 40. she is about to take exam b that has a mean of 650 and a standard deviation of 20. how well must mariana 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.
answer attempt 1 out of 2

Explanation:

Step1: Calculate 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, $x = 338$, $\mu=350$, and $\sigma = 40$. So, $z_A=\frac{338 - 350}{40}=\frac{- 12}{40}=-0.3$.

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

We know that the z - score for Exam B will be the same as the z - score for Exam A since we want equivalent performance. For Exam B, $\mu = 650$, $\sigma=20$, and $z = z_A=-0.3$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$ and solving for $x$, we get $x=z\sigma+\mu$. Substitute $z=-0.3$, $\sigma = 20$, and $\mu = 650$ into the formula: $x=-0.3\times20 + 650$.
$x=-6 + 650=644$.

Answer:

644