Determine the minimum sample size required when you want to be $95 \%$ confident that the sample mean is within one unit of the population mean and $\sigma=11.7$. Assume the population is normally distributed. A 95\% confidence level requires a sample size of (Round up to the nearest whole number as needed.)

Step 1 ：We are given that the standard deviation (σ) is 11.7, the desired margin of error (E) is 1, and the Z-score for a 95% confidence level is approximately 1.96.

Step 2 ：We can use the formula for calculating the sample size for a given confidence level and margin of error: \(n = (Z*σ/E)^2\)

Step 3 ：Substituting the given values into the formula, we get \(n = (1.96*11.7/1)^2\)

Step 4 ：Calculating the above expression, we find that \(n = 526\)

Step 5 ：So, the minimum sample size required for a 95% confidence level and a margin of error of 1, given a standard deviation of 11.7, is \(\boxed{526}\)