Damina\'s Italian Restaurant has one oven to cook pizza. It\'s a large oven; it

Question

Damina's Italian Restaurant has one oven to cook pizza. It's a large oven; it has 5% chance in any one year of being destroyed. If it is destroyed, the machine will cost $7,500 to replace. (Option A)

Damani is considering selling the large oven and buying two smaller ovens. A small oven would cost $3,750 to replace if it is destroyed, and it has a 5% chance of being destroyed. (Option B)

Assuming the cost of operation of the two small machines is the same as the large machine. Which situation faces the most risk?

a. Derive the probability distribution for total losses under option A.

b. Derive the probability distribution for total losses under option B.

c. Compare the amount of risk Damina faces under option A vs. option B. Which option has more risk? Justify and demonstrate your answer.

Explanation / Answer

a) Loss = 0 P(x)=0.95

Loss=7500 P(x)=0.05

Mean=0.05*7500=375

Standard deviation = sqrt(0.05* 7125^2+0.95* 375^2)= 1634.58

b) Mean = 0.05*(3750+3750)=0.375

P(x)

Loss = 7500 P(x)=0.05*0.05

Loss=3750 P(x)=2*0.05*0.95

Loss=0 P(x)= 0.95^2

Standard deviaton = =sqrt( 0.0025*7125^2+2*0.05*0.95*3375^2+0.95*0.95*375^2)=1155.23

Option A has more risk since standard deviation is higher.

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