Step 1 :Given values are: sample mean (\(x_{bar}\)) = 12.9, sample standard deviation (s) = 3.4, sample size (n) = 100, and z-score for 99% confidence interval (z) = 2.576.
Step 2 :Calculate the margin of error using the formula: margin of error = z * (s / \(\sqrt{n}\)).
Step 3 :Substitute the given values into the formula to get: margin of error = 2.576 * (3.4 / \(\sqrt{100}\)) = 0.87584.
Step 4 :Calculate the confidence interval using the formula: lower bound = \(x_{bar}\) - margin of error and upper bound = \(x_{bar}\) + margin of error.
Step 5 :Substitute the values into the formula to get: lower bound = 12.9 - 0.87584 = 12.02416 and upper bound = 12.9 + 0.87584 = 13.77584.
Step 6 :The 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately \(\boxed{[12.02416, 13.77584]}\).