Julia earned a score of 520 on Exam A that had a mean of 450 and a standard deviation of 50. She is about to take Exam B that has a mean of 650 and a standard deviation of 100. How well must Julia 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.
To determine how well Julia must score on Exam B in order to do equivalently well as she did on Exam A, we need to first calculate the z-score for her 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 = Julia's score
μ = mean of the distribution
σ = standard deviation of the distribution
For Exam A:
z = (520 - 450) / 50
z = 70 / 50
z = 1.4
Now, we can use the z-score to find Julia's equivalent score on Exam B:
z = (X - μ) / σ
1.4 = (X - 650) / 100
Solving for X:
1.4 = (X - 650) / 100
140 = X - 650
X = 790
Therefore, Julia must score 790 on Exam B in order to do equivalently well as she did on Exam A.