Assume that an investigation of a process would cost approximately \(\$ 500\). If the process is out-of-control, the cost of correcting the condition would be \(\$ 1,000\). The present value of cost savings over the planning period is estimated to be \(\$ 5,000\).

Required:

(1) If the probability of the process being out-of-control is \(50 \%\), should the process be investigated?

(2) What maximum probability is necessary for the process to be in control in order to warrant an investigation of the process?