Question

Michael earned a score of 630 on Exam A that had a mean of 600 and a standard deviation of 20. He is about to take Exam B that has a mean of 750 and a standard deviation of 40. How well must Michael 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 1

To do equivalently well on Exam B as he did on Exam A, Michael needs to score 810.

Step-by-step explanation:

To do equivalently well on Exam B as he did on Exam A, Michael needs to score at the same level relative to the mean and standard deviation of Exam B as he did on Exam A. To calculate this, we can use the z-score formula which is (X - mean) / standard deviation. Let's calculate the z-score for Michael's score on Exam A:

Z = (630 - 600) / 20 = 1.5

Next, we can use this z-score to find the equivalent score on Exam B:

z = (X - 750) / 40

Solving for X:

1.5 = (X - 750) / 40

1.5 * 40 = X - 750

60 = X - 750

X = 810

Therefore, Michael needs to score 810 on Exam B in order to do equivalently well as he did on Exam A.