A professor standardizes exam scores so that all exams have μ = 50 and σ = 10.If the original scores from an exam have μ = 42 and σ = 6,then a student with an original exam score of X = 45 would receive a standardized score of X = 55.

Question

Quizplus · Accepted Answer

To standardize a score, we use the following formula:

z = (X - μ) / σ

where X is the original score, μ is the mean of the population, and σ is the standard deviation of the population.

In this case, the professor standardized the scores so that μ = 50 and σ = 10. The original scores had μ = 42 and σ = 6.

To find the standardized score for X = 45, we use the formula:

z = (X - μ) / σ = (45 - 42) / 6 = 0.5

This means that the original score of 45 is 0.5 standard deviations above the mean of the original scores.

To find the standardized score for this student, we use the formula:

X = z * σ + μ = 0.5 * 10 + 50 = 55

Therefore, the student with an original score of X = 45 would receive a standardized score of X = 55. So, the statement is true.

A Professor Standardizes Exam Scores So That All Exams Have