A local contractor manufactures the speakers used in telephones. The phone company requires the speakers to ring at a specified noise level (in decibels). An X

chart is being designed to monitor this variable. The process of sampling speakers from the line requires hitting the speakers with a fixed-force clapper and measuring the decibel level on a meter designed for that purpose. The cost of sampling is

$1.25 per speaker. When the process goes out of control, the thickness of the speakers is incorrect. The cost of searching for an assignable cause is estimated to be $50. The cost of operating the process in an out-of-control state is estimated to be $180 per hour. Out of control corresponds to a shift of 2 in the decibel level, and the probability that the process shifts out of control in any hour is .03.

a. The company uses an X chart based on 3 limits and subgroups of size