malik earned a score of 316 on exam a that had a mean of 300 and a standard deviation of 40. he is about to…
malik earned a score of 316 on exam a that had a mean of 300 and a standard deviation of 40. he is about to take exam b that has a mean of 700 and a standard deviation of 25. how well must malik 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.
Answer
Explanation:
Step1: Calculate 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, $x = 316$, $\mu=300$ and $\sigma = 40$. So, $z_A=\frac{316 - 300}{40}=\frac{16}{40}=0.4$.
Step2: Use the z - score to find the score on Exam B
We want the z - score on Exam B, $z_B$ to be equal to $z_A$. For Exam B, $\mu = 700$, $\sigma=25$ and $z_B = 0.4$. Using the z - score formula $z=\frac{x-\mu}{\sigma}$ and solving for $x$, we get $x=z_B\sigma+\mu$. Substitute $z_B = 0.4$, $\sigma = 25$ and $\mu = 700$ into the formula: $x=0.4\times25 + 700$. $x = 10+700=710$.
Answer:
710