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: \(n = (Z*σ/E)^2\) where: Z is the z-score corresponding to the desired confidence level (for a 95% confidence level, Z = 1.96), σ is the standard deviation of the population, E is the desired margin of error.
Step 3 :We can plug in the given values into this formula to find the required sample size. Given that the mean = 1500, standard deviation = 300, margin of error = 25, and z-score = 1.96.
Step 4 :By substituting the given values into the formula, we get the sample size = 554.
Step 5 :Final Answer: The number of students that should be sampled is \(\boxed{554}\).