SAT scores are distributed with a mean of 1,500 and a standard deviation of 288. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your confidence interval to 40 points with 85 percent confidence, how many students should you sample? (Round up to a whole number of students.)

Step 1 ：We are given that the SAT scores are distributed with a mean of 1,500 and a standard deviation of 288. We are interested in estimating the average SAT score of first year students at a college. We want to limit the margin of error of our confidence interval to 40 points with 85 percent confidence.

Step 2 ：To find out how many students we should sample, we can use the formula for the sample size in a confidence interval estimation: \(n = (Z*σ/E)^2\), where \(n\) is the sample size, \(Z\) is the Z-score corresponding to the desired confidence level, \(σ\) is the standard deviation of the population, and \(E\) is the desired margin of error.

Step 3 ：In this case, we know that \(σ = 288\), \(E = 40\), and we want a confidence level of 85%. The Z-score for an 85% confidence level is approximately 1.44.

Step 4 ：Plugging these values into the formula, we get \(n = (1.44*288/40)^2\).

Step 5 ：Calculating the above expression, we find that \(n = 108\). Since we can't have a fraction of a student, we'll round up to the nearest whole number if we get a decimal.

Step 6 ：Final Answer: The number of students that should be sampled is \(\boxed{108}\).