Step 1 :We are given that the population standard deviation (\(\sigma\)) is 24.7, the desired margin of error (E) is 10, and the Z-score (Z) for a 95% confidence level is 1.96.
Step 2 :We need to find the sample size (n) using the formula: \(n = (Z*\sigma/E)^2\)
Step 3 :Substituting the given values into the formula, we get: \(n = (1.96*24.7/10)^2\)
Step 4 :Calculating the above expression, we find that the required sample size is \(\boxed{24}\).