Part a
Required 95% confidence interval by using Minitab is given as
below:
Variable        Â
N     Mean   Â
StDev  SE Mean
Time           Â
27Â Â Â Â 43.89Â Â Â Â
25.28Â Â Â Â Â 4.87
Variable           Â
95.0%
CIÂ Â Â Â Â Â Â Â Â Â Â
Time        Â
(  33.89,  53.89)   Â
Confidence interval = (33.89, 53.89)
Part b
The assumption of normality we must make about the population
distribution in order to construct the above confidence
interval.
Part c
Yes, assumption needed in order to construct the confidence
interval is valid because the variable total processing time is
approximately normally distributed.
