When a production machine is properly calibrated, it requires an average of 25 seconds per unit produced, with a standard deviation of 3 seconds. For a simple random sample of n 5 36 units, the sample mean is found to be }x 5 26.2 seconds per unit.
a. What z-score corresponds to the sample mean of }x 5 26.2 seconds?
b. When the machine is properly calibrated, what is the probability that the mean for a simple random sample of this size will be at least 26.2 seconds?
c. Based on the probability determined in part (b), does it seem likely that the machine is properly calibrated? Explain your reasoning.