4.86 A contractor estimates the probabilities for the number of days required to complete a certain type of construction project as follows:

Time (days) 1 2 3 4 5 Probability 0.05 0.20 0.35 0.30 0.10

a. What is the probability that a randomly chosen project will take less than 3 days to complete?

b. Find the expected time to complete a project.

c. Find the standard deviation of time required to complete a project.

d. The contractor’s project cost is made up of two parts—a fixed cost of $20,000, plus $2,000 for each day taken to complete the project. Find the mean and standard deviation of total project cost.

e. If three projects are undertaken, what is the probability that at least two of them will take at least 4 days to complete, assuming independence of individual project completion times?