1. The overall mean completion time for 100 replications of a service procedure is 6.6 hours, with a standard deviation of 2.3 hours. The replication completion times are normally distributed.
   1. Calculate the 95% confidence interval for the long-run expected average completion time. (10 points)
   2. Calculate the 95% prediction interval for the average completion time on any particular day. (10 points)
   3. Explain the observed difference between the confidence interval and prediction interval. (10 points)
   4. Suppose we were to increase the number of replications to 500 and the mean completion time and standard deviation remained the same.
      1. Calculate the 95% confidence interval for the long-run expected average completion time. (10 points)
      2. Explain the observed difference between the confidence intervals for parts 1.a and 1.d.i. (5 points)
      3. Discuss the limit for the confidence interval if we were to continue to increase the number of replications. (5 points)