Required within 4 Hours – Urgent

1)
How does knowing how to calculate probability help the safety professional in measuring safety performance? (No more than one paragraph.) 
2)
Question has two parts.  Suppose you a selecting a new vendor that inspects your facilities fire extinguishers, eye wash stations and stock first aid cabinets on a monthly basis.  You could pay them an up-front, lump sum of $48,000 for three years worth of service, or pay monthly installments of $1473 for 36 months.  In three years, at the end of the 36 month agreement, you will have paid $53,028.  Part I (4 Points). If one were to ignore the fact that the $48,000 could be put in a high-interest investment, and simply consider inflation at 2.5% annually over the next three years, what is the future value of the $48,000 lump sum in three years?  Part II (1 Point).  In one or two sentences, state whether it makes sense to pay the new vendor a lump sum, cash payment of $48,000 up front, and why. 

3)
Why is it important for safety professionals to know fundamental financial metrics when discussing safety performance?  (No more than one paragraph.) 

4)
Suppose a new ergonomic, safety intervention cost $405,000.  Further suppose the intervention is certain to prevent all back injuries associated with the job.  Over the last three years, the employer has averaged 14 injuries per year, with an average cost of $14,000 per injury.  What would be the ROI for a three-year period for this intervention? 

5)
 Suppose a new initiative in safety cost 5,000.  The investment saved the employer $278,000.  What is the ROI for the new initiative?

6)
 Suppose a chemical company has a pressure vessel (i.e., tank) for heating methyl ethyl doo doo.  The pressure vessel is equipped with a sensor that sends a reading of the pressure to an operator employee in a control room.  When the operator notices the pressure exceeding a safe level, the employee is to operate controls to transfer methyl ethyl doo doo from the vessel before an explosion occurs.  The control room panel is also equipped with an alarm should the operator fail to notice the pressure is getting too high and fail to transfer methyl ethyl doo doo right away.  As an additional backup to prevent an explosion, the pressure vessel is also equipped with a relief valve that should operate before pressure reaches a level that would cause the vessel to explode.  In essence, assume there are three mechanisms in place to prevent explosion:  1) the sensor that sends a signal to the control panel; 2) the alarm on the control panel; and 3) the relief valve.  All three must fail in order for an explosion to occur.  Presume the failure rates of each are as follows:  1) sensor = 0.005;  2) the alarm = 0.003; and 3) the relief valve = 0.002.  If one were to disregard probability of human error (i.e., the operator fails to notice the sensor because she/he is distracted), what is the probability of an explosion due to failure of the electronic and mechanical components of the pressure vessel system? 

7)
 Suppose a machine has two components that prevent injury; component A and component B.  If either of the components fail, an employee will be injured. It is important to note that both A and B cannot fail at the same time.  (In other words, they are mutually exclusive events.) If the failure rate for component A is 0.0005 and component B is 0.004, what is the probability an employee will be injured because of failure of these components?