You work for the infrastructure department in the state of Kansas and were tasked to evaluate whether to use a larger diameter pipe for a water line. This lager diameter pipe will cost $400,000 more initially, but will reduce pumping costs. The optimistic, most likely, and pessimistic projections for annual savings are $100,000, $80,000, and $30,000, with 0.15, 0.50, and 0.35 probability, respectively. Furthermore, you are not sure about which minimum attractive rate of return (MARR) to use in your analysis but were informed by your boss that MARR can be 12% with 0.25 probability, 15% with 0.55 probability, or 18% with 0.20 probability. The water line should have a life of 45 years.

a) Calculate the expected value of present worth EV(PW).

b) Compute the present worth of the expected value PW(EV).

c) Do the answers from a) and b) match? Why or why not?

d) Calculate the present worth's standard deviation (sigma).