Grayson earned a score of 45 on Exam A that had a mean of 73 and a standard deviation of 20. He is about to take Exam B that has a mean of 700 and a standard deviation of 25. How well must Grayson 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.
To find the equivalent score on Exam B, we need to first calculate Grayson's z-score on Exam A and then use that z-score to find the equivalent score on Exam B.
The z-score formula is:
z = (X - μ) / σ
where:
X = Grayson's score
μ = mean
σ = standard deviation
For Exam A:
z = (45 - 73) / 20
z = -28 / 20
z = -1.4
Now we can use the z-score to find the equivalent score on Exam B:
z = (X - μ) / σ
-1.4 = (X - 700) / 25
Solving for X:
-1.4 * 25 = X - 700
-35 = X - 700
X = -35 + 700
X = 665
Therefore, Grayson must score a 665 on Exam B to do equivalently as he did on Exam A.