Management Is Currently Deciding Whether or Not to Investigate a Cost

Management is currently deciding whether or not to investigate a cost variance that was identified by the accounting system.To help address this question,you have generated the following data:
Possible States of Nature:
1.The underlying operation is in control (i.e. ,is operating normally).
2.The underlying operation is out of control (and therefore is in need of an intervention)
Possible Decisions/Courses of Action:
1.Investigate the variance (to determine its underlying cause(s)).
2.Do not investigate the variance
Estimated Costs and Probabilities:
1.Cost of investigating the variance = I = $5,000.
2.Cost of correcting an out-of-control process (if the process is found to be out of control)= C = $10,000.
3.Losses from not correcting an out-of-control process = L = $110,000.
4.Probability,p,of the process being out of control = 60%
Required: 1.Recast the above information in a payoff table.
2.What is the expected cost of the decision to investigate the variance? Show calculations.
3.What is the expected cost of the decision to not investigate the variance? Show calculations.
4.What is the break-even probability of the process being out of control,p,that would make management indifferent between investigating and not investigating the observed variance? Demonstrate that,in fact,this is the break-even probability by showing the expected value of each management action.Show calculations.