A contractor estimates the probabilities for the num- ber of days required to complete a certain type of con- struction 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.

Question

A contractor estimates the probabilities for the num- ber of days required to complete a certain type of con- struction 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 prob- ability that at least two of them will take at least 4 days to complete, assuming independence of indi- vidual project completion times?

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