SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). Consider the following two problems, which appear at a glance to be very similar. Which one requires the application of the Central Limit Theorem, and in what way does the solution process differ between the two problems? (a)If a student is randomly selected, what is the probability that his or her score is above 500? (b)If a sample of 35 students is selected randomly, what is the probability that the sample mean will be above 500?

Question

Quizplus · Accepted Answer

The Answer is The first problem involves the formula

z = \frac { x - \mu } { \sigma }

, whereas the second involves the Central Limit Theorem and the formula

\mathrm { z } = \frac { \bar { x } - \mu } { \frac { \sigma } { \sqrt { n } } }

since it concerns a sample.

SAT Verbal Scores Are Normally Distributed with a Mean of 430