Rock band The Rolling Stones have played scores of concerts in the last twenty years. For $30$ randomly selected Rolling Stones concerts, the mean gross earnings is $2\mathrm{.}42$ million dollars.

Part a$)$ Assuming a population standard deviation gross earnings of $0\mathrm{.}45$ million dollars, obtain a $99\%$ confidence interval for the mean gross earnings of all Rolling Stones concerts $($in millions$).$ Please carry at least three decimal places in intermediate steps. Give your answer to the nearest $3$ decimal places.

Confidence interval: $($

$.$

Part b$)$

Which of the following is the correct interpretation for your answer in part $($a$)?$

A$.$ We can be $99\%$ confident that the mean gross earnings for this sample of $30$ Rolling Stones concerts lies in the interval

B$.$ There is a $99\%$ chance that the mean gross earnings of all Rolling Stones concerts lies in the interval

C$.$ If we repeat the study many times, $99\%$ of the calculated confidence intervals will contain the mean gross earning of all Rolling Stones concerts.

D$.$ None of the above