2. An energy drink company routinely measures the caffeine content of their drinks. Suppose that the complay selects 100 samples of the drink every hour from it's production line and determinesthe caffeine content. From previous analyses, the company is confident that the caffeine content has a normal distribution with = 6.8mg. During a one hour period, the 100 samples yielded a mean caffeine content of = 130mg (a) Construct a 95% confidence interval for the mean caffeine content of the energy drink produced during the hour in which the samples were taken. (b) What would happen to the width of the of the confidence interval if our confidence level changed for this interval went from 95% to 99%? Explain why this makes sense. (c) What would happen to the width of the confidence interval if we were to double sample size from 100 to 200? Explain why this makes sense (No need to construct a new confidence interval). (d) Suppose the company repeats this process every hour of every day for one week, thus constructing 40 separate confidence intervals for the estimated mean caffeine content of their drinks. Of these intervals, how many would you expect to fail to contain the value of thus providing an inaccurate estimation of the mean caffeine content? 1