Question

Madeline earned a score of 410 on Exam A that had a mean of 650 and a standard deviation of 100. She is about to take Exam B that has a mean of 700 and a standard deviation of 25. How well must Madeline 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

Madeline needs to score a 640 on Exam B to perform equivalently to her score on Exam A, based on the calculation of her z-score from Exam A and applying it to the statistics of Exam B.

Step-by-step explanation:

To determine how well Madeline must score on Exam B to do equivalently as well as she did on Exam A, we calculate the z-score of her Exam A score and apply it to the statistics of Exam B.

First, find the z-score for Madeline's score on Exam A:

Z = (Score - Mean) / Standard Deviation

Z = (410 - 650) / 100

Z = -2.4

This z-score represents how many standard deviations Madeline's score is from the mean on Exam A. To find the equivalent score on Exam B, we apply this z-score to the statistics for Exam B.

Score on Exam B = Mean of Exam B + (Z * Standard Deviation of Exam B)

Score on Exam B = 700 + (-2.4 * 25)

Score on Exam B = 700 - 60

Score on Exam B = 640

Madeline needs to score a 640 on Exam B to perform equivalently to how she did on Exam A.