CHAPTER PROBLEMS $1.$ Describe the difference between chance and assignable causes. $2.$ How would you use variation to manage a group of people? Why should a manager be aware of assignable and chance causes? $3.$ Select one of the tools taught in this chapter and describe why applying it to problems in your future will enhance your ability to solve those problems. X AND R CHARTS $4.$ A large bank establishes X and R charts for the time required to process applications for its charge cards. A sample of five applications is taken each day. The first four weeks $(20$ days$)$ of data give X $=16$ min, s $=3$ min $,$ R $=7$min Based on the values given, calculate the centerline and control limits for the X and R charts. $5.$ Steering wheels in many vehicles are outfitted with an airbag and horn as well as switches for controlling radio volume, cruise control, and other devices. Connecting these devices and switches to a steering wheel requires excellent positioning control during assembly. For this reason, hole location is closely monitored in the X$,$ Y$,$ and Z directions. The data below are X and R values for $25$ samples of size n $=4$ for hole location data for the X$-$axis dimension.