The Chartered Financial Analyst $($CFA$)$ designation is fast becoming a requirement for serious investment

professionals. Although it requires a successful completion of three levels of grueling exams, the

designation often results in a promising career with a lucrative salary. A student of finance is curious about

the average salary of a CFA charterholder. He takes a random sample of $36$ recent charterholders and

computes a mean salary of $$146,000$ with a standard deviation of $$23,000.$ Use this sample information to

determine the $99\%$ confidence interval for the average salary of a CFA charterholder.

Note: Round your final answers to the nearest whole number.

Confidence interval