Question

yaritza earned a score of 850 on exam a that had a mean of 750 and a standard deviation of 50. she is about to take exam b that has a mean of 29 and a standard deviation of 4. how well must yaritza 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 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, $x = 850$, $\mu=750$, and $\sigma = 50$.
$z_A=\frac{850 - 750}{50}$
$z_A=\frac{100}{50}=2$

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

We know that the z - score for Exam B should be the same as the z - score for Exam A since we want equivalent performance. For Exam B, $\mu = 29$, $\sigma=4$, and $z_B = z_A=2$.
Using the z - score formula $z=\frac{x - \mu}{\sigma}$ and solving for $x$, we get $x=z\sigma+\mu$.
$x = 2\times4+29$
$x=8 + 29=37$

Answer:

37