MEANS Confidence Intervals: Generate the specified confidence interval. Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 100 cookies and finds that the number of chocolate chips per cookio in the sample has a mean of 12.9 and a standard deviation of 3.4. What is the $99 \%$ confidence interval for the number of chocolate chips per cookie for Big Chip cookies?
Answer
The 99% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately \(\boxed{[12.02416, 13.77584]}\).
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 \(\boxed{[12.02416, 13.77584]}\).
