Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advices and support from the accountant if the client were audited. A large accounting firm is trying to determine what fee to charge for next$$ year's returns. In previous$$ years, the actual mean cost to the firm for attending a client audit session was $$$$710.$ To determine if this cost has$$ changed, the firm randomly samples $37$ client audit fees. The sample mean audit cost was $$$$680$ with a standard deviation of $$$$85.$ Complete part a below

a$)$ Develop a $99\%$ confidence interval estimate for the mean audit cost.