Step 1 :Given values are: mean score (\(\mu\)) = 79, standard deviation (\(\sigma\)) = 3.8, sample size (\(n\)) = 25, and Z-score for 98% confidence interval (\(Z_c\)) = 2.33.
Step 2 :Calculate the margin of error (\(E\)) using the formula: \(E = Z_c \times \frac{\sigma}{\sqrt{n}}\).
Step 3 :Substitute the given values into the formula: \(E = 2.33 \times \frac{3.8}{\sqrt{25}}\) which simplifies to \(E = 1.77\).
Step 4 :Calculate the confidence interval using the formula: \(\mu \pm E\).
Step 5 :Substitute the given values into the formula: lower bound = \(79 - 1.77 = 77.23\) and upper bound = \(79 + 1.77 = 80.77\).
Step 6 :The 98% confidence interval for the mean is \(\boxed{(77.23, 80.77)}\).