J. Namias used the techniques of statistical quality control to determine when to conduct a search for specific causes of consumer complaints at a beverage company (Journal of Marketing Research, Aug. 1964). Namias discovered that when the process was in control, the biweekly complaint rate of a bottled product (i.e., the number of customer complaints per 10,000 bottles sold in a 2-week period) had an approximately normal distribution with μ = 26 and σ = 11.3. Customer complaints primarily concerned chipped bottles that looked dangerous.

a. Find a tolerance interval for 99% of the complaint rates when the bottling process is assumed to be in control. What is the confidence coefficient for the interval? Explain. 

b. In one 2-week period, the observed complaint rate was 93.12 complaints per 10,000 bottles sold. Based on your knowledge of statistical quality control, do you think the observed rate is due to chance or some specific cause? In actuality, a search for a possible problem in the bottling process led to a discovery of rough handling of the bottled beverage in the warehouse by newly hired workers. As a result, a training program for new workers was instituted.