Question

A contractor has submitted bids on three state jobs: an office building, a theater, and a parking
garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contrac-
tor is awarded any of these jobs, the profits earned from these contracts are $10 million from the of-
fice building, $5 million from the theater, and $2 million from the parking garage. His profit is zero
if he gets no contract. The contractor estimates that the probabilities of getting the office building
contract, the theater contract, the parking garage contract, or nothing are. 15, .30, .45, and .10, respec-
tively. Let x be the random variable that represents the contractor's profits in millions of dollars. Write
the probability distribution of x. Find the mean and standard deviation of x. Give a brief interpretation
of the values of the mean and standard deviation.

Answer 1

Answer:

P(x = 10) = P(office contract) = 0.15 P(x = 5) = P(theater contract) = 0.3 P(x = 2) = P(garage contract) = 0.45 P(x = 0) = P(no job) = 0.10 Mean of x = E(x) = 10P(x = 10) + 5P(x = 5) + 2P(x = 2) + 0P(x = 0) + 0 = 10(0.15) + 5(0.3) + 2(0.45) + 0(0.10) + 0 = 3.9 If this experiment is repeated a large number of times, on average the contractor would earn near 3.9 million dollars per trial. St. dev. of x = sqrt(Var(x)) = sqrt[E(x^2) - (E(x))^2] = sqrt[sum over n of n^2 P(x = n) - (3.9)^2] = sqrt[(10^2 P(x = 10) + 5^2 P(x = 5) + 2^2 P(x = 2) + 0^2 P(x = 0) + 0) - (3.9)^2] = sqrt[100(0.15) + 25(0.3) + 4(0.45) + 0(0.10) + 0 - (3.9)^2] = sqrt(15 + 7.5 + 1.8 - 15.21) = sqrt(9.09) or about 3.015. If this experiment is repeated a large.