Question: A construction company has to complete a project no later than three months from now or there will be significant cost overruns. The manager of the construction company believes that there are four possible values for the random variable X, the number of months from now it will take to complete this project: 2, 2.5, 3, and 3.5. The manager currently thinks that the probabilities of these four possibilities are in the ratio 1 to 2 to 4 to 2. That is, X = 2.5 is twice as likely as X = 2, X = 3 is twice as likely as X = 2.5, and X = 3.5 is half as likely as X = 3.

a. Find the probability distribution of X.

b. What is the probability that this project will be completed in less than three months from now?

c. What is the probability that this project will not be completed on time?

d. What is the expected completion time (in months) of this project from now?

e. How much variability (in months) exists around the expected value you found in part d?