A manufacturing company wants to ensure that the majority of parts are produced within a certain tolerance. Based on customer specifications, the company has determined that this tolerance is between 35 and 40 units. A large sample of data points collected revealed an average of 36 units with a standard deviation of 1.5 units.
Calculate the process capability index and advise if the process is at an acceptable level for an existing process (defend your answer). Please show all calculations.