Question: A manufacturing facility needs to open a new assembly line in four months or there will be significant cost overruns. The manager of this project

A manufacturing facility needs to open a new assembly line in four months or there will be significant cost overruns. The manager of this project believes that there are four possible values for the random variableX(the number of months from now it will take to complete this project): 3, 3.5, 4, and 4.5. It is currently believed that the probabilities of these four possibilities are in the ratio 1 to 2 to 3 to 2. That is,X= 3.5 is twice as likely asX= 3 andX= 4 is 1.5 times as likely asX= 3.5.

Find the probability distribution ofX.

What is the probability that this project will be completed in less than 4 months from now?

What is the probability that this project willnotbe completed on time?

What is the expected completion time (in months) from now for this project?

How much variability (in months) exists around the expected value found in (A)?

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