The life in hours of a thermocouple used in a furnace is known to be approximately normally distributed, with standard deviation = 20 hours. A random sample of 15 thermocouples resulted in the following data: 553, 552, 567, 579, 550, 541, 537, 553, 552, 546, 538, 553, 581, 539 and 529. a. Construct a 95% two-sided confidence interval (CI) for the mean life of all the thermocouples used in the furnaces. b. Interpret the CI obtained in part a. c. Construct a 95% one-sided confidence interval with an upper bound for the mean life of all the thermocouples used in the furnaces. d. Interpret the CI obtained in part c. e. If we would like to estimate the mean life of all the thermocouples used in the furnaces with an error that is less than 3 hours at 98% confidence. What sample size is required