Question

Ellie earned a score of 590 on Exam A that had a mean of 650 and a standarddeviation of 25. She is about to take Exam B that has a mean of 63 and a standarddeviation of 20. How well must Ellie score on Exam B in order to do equivalently wellas she did on Exam A? Assume that scores on each exam are normally distributed.

Answer 1

Answer

15

Ellie needs to score 15 on Exam B in order to do equivalently as well as she did on Exam A.

Explanation

Since both distributions are normally distributed, we will use the standardized scores of Ellie on both exams to answer this question.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ

where

z = standardized score or z-score

x = score in the distribution or in the exam

μ = Mean

σ = Standard deviation

So, we will find the standardized score on Exam A and use that standardized score to find the equivalent score on exam B.

For exam A,

z = ?

x = 590

μ = 650

σ = 25

z = (x - μ)/σ

z = (590 - 650)/25

z = (-60/25) = -2.4

For exam B, to find the equivalent score with a standardized score of -2.4

z = -2.4

x = ?

μ = 63

σ = 20

z = (x - μ)/σ

-2.4 = (x - 63)/20

(x - 63)/20 = -2.4

Cross multiply

x - 63 = (20) (-2.4)

x - 63 = -48

x = 63 - 48

x = 15

Hope this Helps!!!