Question

question
nabhitha earned a score of 680 on exam a that had a mean of 700 and a standard deviation of 50. she is about to take exam b that has a mean of 100 and a standard deviation of 10. how well must nabhitha 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 score, $\mu$ is the mean, and $\sigma$ is the standard deviation. For Exam A, $x = 680$, $\mu=700$, and $\sigma = 50$.
So, $z_{A}=\frac{680 - 700}{50}=\frac{- 20}{50}=- 0.4$.

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

For Exam B, we know that $z = z_{A}=-0.4$, $\mu = 100$, and $\sigma=10$. We use the z - score formula $z=\frac{x - \mu}{\sigma}$ and solve for $x$.
Rearranging the formula for $x$ gives $x=\mu+z\sigma$.
Substitute the values: $x = 100+(-0.4)\times10=100 - 4 = 96$.

Answer:

96