A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed. The proportion of scores that lie between 460 and 600 is _________.
A) 0.4394
B) 0.5365
C) 0.4406
D) 0.4635

Question

Quizplus · Accepted Answer

To find the proportion of scores between 460 and 600, we use the Z-score formula: Z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. For X = 460, Z = (460 - 500) / 90 = -40 / 90 = -0.444. For X = 600, Z = (600 - 500) / 90 = 100 / 90 = 1.111. Looking these Z-scores up in a standard normal distribution table or using a calculator, we find the areas (proportions) to the left of each Z-score. The difference between these areas gives the proportion of scores between 460 and 600. This calculation results in approximately 0.5365, which matches option B.

A Testing Bureau Reports That the Mean for the Population