Bolton, Inc., an Internet service provider $($ISP$),$ has

experienced rapid growth in the past five years. As a

part of its marketing strategy, the company promises

fast connections and dependable service. To achieve its

objectives, the company constantly evaluates the

capacity of its servers. One component of its evaluation

is an analysis of the average amount of time a customer

is connected and actively using the Internet daily. A

random sample of $12$ customer records shows the

following daily usage times, in minutes:

$268336296311306335$

$301278290393373329$

a$.$ Using the sample data, compute the best point

estimate of the population mean for daily usage

times for Bolton$$s customers.

b$.$ The managers of Bolton$$s marketing department

would like to develop a $99\%$ confidence interval

estimate for the population mean daily customer