A manufacturer supplies a certain type of assembly to customers. The manufacturer recognizes the advantages of control charts and uses them consistently. In the past month, its X and R charts for the assembly indicated a process well within control. For these charts, 100 subsamples of size n = 5 each were used. In addition, the manufacturer compared the 100 X's to the specification limits set by one of its customers. Only 2 out of these 100 averages were outside the specification limits. This was good news because the customer was willing to accept orders with no more than 5% out of specifications. However, the manufacturer was shocked when the customer rejected an order for 1000 assemblies. The customer claimed that it inspected 50 of the 1000 assemblies, and 10% (i.e., 5) of them were out of specifications. What is going on here? Is it likely that the customer could see so many bad assemblies, given what the manufacturer observed in its process? Perform appropriate calculations, and write up your results in a short report. Make whatever assumptions you deem relevant.