Score: $15 / 30 \quad 4 / 6$ answered Question 6 SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. 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 $95 \%$ confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer.

Step 1 ：The problem is asking for the sample size needed to estimate the average SAT score with a certain level of confidence and margin of error. This is a problem of determining sample size for estimating a population mean.

Step 2 ：The formula for the sample size n is given by: \(n = \left( \frac{Z \cdot \sigma}{E} \right)^2\) where: Z is the z-score corresponding to the desired level of confidence, σ is the standard deviation of the population, and E is the desired margin of error.

Step 3 ：For a 95% confidence level, the z-score is approximately 1.96. The standard deviation σ is given as 300, and the desired margin of error E is 25.

Step 4 ：We can substitute these values into the formula to find the required sample size. Note that we should round up to the nearest whole number, since we can't have a fraction of a student.

Step 5 ：Final Answer: The number of students that should be sampled is \(\boxed{554}\).