For the first problem of the homework, please help me complete the following usi

Question

For the first problem of the homework, please help me complete the following using normal distribution and draw a cash flow diagram for each option. For the first problem of the homework, please help me complete the following using normal distribution and draw a cash flow diagram for each option. For the first problem of the homework, please help me complete the following using normal distribution and draw a cash flow diagram for each option. A city's wastewater treatment plant needs a new filter system. Two options are being considered. For option A, the amount of total dissolved solids (TDS) left after filtration is normally distributed with a mean of 8 ppm and a standard deviation of 2 ppm. For option B, the amount of TDS left after filtration is normally distributed with a mean of 1 ppm and a standard deviation of 1 ppm. The performance of each filter is based on the amount of TDS left (see Table 1). Table 1: Performance rating, criteria and cost for total dissolved solids in drinking water Costs Associated with Performance (S per capita each year) 2.5 1.25 0.05 Performance TDS after filtration (ppm) Poor Good Excellent TDS-7 ppm 4-TDSs7 ppm TDSs4 ppm Option A costs $7.50 per capita to install, $2.00 per capita each year to maintain, and has a service life of 10 years. Option B costs $10.50 per capita to install, $3.00 per capita each year to maintain, and has a service life of 20 years. The costs associated with the performance level must also be added for both filter alternatives. Based on expected monetary value and an interest rate of 10 percent, which option should the city choose? Use a decision tree to set up your solution (fill in all probabilities and monetary values) and show all of your work You can decide on which method from engineering economics to use to compare costs

Explanation / Answer

Option A has N(8,2) and option B has N(4,1), the rating changes at 4 and 7, thus we require probabilities for P(x>7) and P(x<4).

For option A, P(x>7), statistic is (7-8)/2= -0.5 the probabilty comes to be 69.15% for P(x<4), statitic is -4/2=-2, the probability is 2.28%

For option B, P(x>7), statistic is (7-4)/1= 3 the probabilty comes to be 0.13 % for P(x<4), statitic is 0, the probability is 50%

Costs thus are for option A=7.5+2*10+10*(0.6915*2.5+0.0228*0.05+0.2857*1.25)=48.37

for option A=10.5+3*10+10*(0.0013*2.5+0.5*0.05+0.4987*1.25)=47.01

Thus option B is cheaper.

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