made a purchase on the website yielded a mean of $$2000$ and a standard deviation of $$150.$ Complete parts $($a$)$ and $($b$)$ below.

a$.$ Construct a $99\%$ confidence interval estimate for the mean spending for all shoppers who are members of the website's premium program.

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$($Round to two decimal places as needed.$)$

b$.$ Interpret the interval constructed in $($a$).$

Choose the correct answer below.

A$.$ The sample mean spending in $99\%$ of all samples of $96$ members of the website's premium program will be between the lower and upper limits of the confidence interval.

B$.99\%$ of all shoppers who are members of the website's premium program have spent an amount in dollars that is between the lower and upper limits of the confidence interval.

D$.$ With $99\%$ confidence, the mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval.