In project management it is important to understand key constraints, e$.$g$,$ cost$,$ time and quality. In

particular, ability to properly estimate prolect completion time and cost are critical for the company s

reputation. It can be done based on historical data from similar past projects. Let's assume that project

quality is not affected by project costs or its duration.

The initial phase of a construction project entails three activities that must be undertaken sequentially

$($that is the next activity cannot begin until the previous one is complete$)$ and the time to complete each

activity is a random variable with the following parameters.

Activity

Excavation

Foundations

Structural steel

Mean $($u$)$

$21$

IS

$48$

Std$.$ Deviation $($o$)$

Find the expected time of project completion and the range of possible completion times, assuming they

follow distributions with means and standard deviations listed in the table. Assume also that the project

costs C $=$ Co $+$d$*5,000,$ where fixed cost Co$=$ $$15,000$ and d is the number of days a project need for

completion. Given previous results, calculate expected project cost and its standard deviation.

$1.$ What is the mean time to complete the project?

$2.$ What is the standard deviation of the completion time for the entire project?

$3.$

What are possible project completion times with $95\%$ probability? Hint: Use Empirical Rule.

$4.$

What is expected cost of the project?

$5.$

What is the standard deviation of the project cost?