Question

Tamika earned a score of 255 on Exam A that had a mean of 250 and a standard deviation of 25. She is about to take Exam B that has a mean of 200 and a standard deviation of 40. How well must Tamika 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.

Answer 1

To determine how well Tamika must score on Exam B to perform equivalently to Exam A, we need to compare the scores relative to their respective means and standard deviations.

Let's start by calculating the z-score for Tamika's score on Exam A:

z-score_A = (x - mean_A) / standard deviation_A

Substituting the given values:
z-score_A = (255 - 250) / 25
z-score_A = 0.2

Now, we can find the corresponding score on Exam B using the z-score and the parameters of Exam B:

z-score_B = (x - mean_B) / standard deviation_B

Since we want Tamika to perform equivalently, the z-scores for both exams should be equal:

0.2 = (x - 200) / 40

Solving for x, the score Tamika must achieve on Exam B:

x - 200 = 0.2 * 40
x - 200 = 8
x = 208

Therefore, Tamika must score 208 on Exam B in order to perform equivalently as she did on Exam A.