Step 1 :We are given that the sample mean (x̄) is 33.30 thousand dollars and the standard deviation (σ) is 10.7 thousand dollars. The sample size (n) can be calculated by counting the number of data points.
Step 2 :The formula for a confidence interval is \(x̄ ± Z * (σ/√n)\), where Z is the Z-score corresponding to the desired confidence level. For a 75% confidence interval, the Z-score is approximately 1.15.
Step 3 :Calculate the sample size by counting the number of data points. The sample size (n) is 42.
Step 4 :Plug the values into the formula to find the lower and upper limits of the confidence interval. The lower limit is approximately 31.40 thousand dollars and the upper limit is approximately 35.20 thousand dollars.
Step 5 :The 75% confidence interval for the average annual profit per employee for all successful banks is approximately \(\boxed{[31.40, 35.20]}\) thousand dollars.