SAT Verbal Scores Are Normally Distributed with a Mean of 430

question 44

Essay

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). (a)If a single student is randomly selected,
find the probability that the sample mean is above 500. (b)If a sample of 35 students are
selected randomly, find the probability that the sample mean is above 500. These two
problems appear to be very similar. Which problem requires the application of the central
limit theorem, and in what way does the solution process differ between the two problems?

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Definitions:

Sales Variance

The difference between actual sales and budgeted or forecasted sales.

Sales Price Variance

The difference between the actual sales price of a product and its expected (or standard) sales price.

Sales Volume Variance

The difference between the actual quantity sold and the budgeted quantity sold, multiplied by the standard selling price per unit.

Purchasing Department

The division within a company responsible for acquiring goods and services necessary for the business operations.