A contractor is interested in the total cost of a project on which she intends to bid. She estimates that materials will cost $25,000 and that her labor will be $900 per day. If the project takes X days to complete, the total labor cost will be 900X dollars, and the total cost of the project (in dollars) will be as follows:

C = 25,000 + 900X Using her experience the contractor forms probabilities (Table 4.4) of likely completion times for the project.

a. Find the mean and variance for completion time X.

b. Find the mean, variance, and standard deviation for total cost C.

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Table 4.4 Probability Distribution for Completion Times COMPLETION TIME X (DAYS) 10 11 12 13 14 Probability 0.1 0.3 0.3 0.2 0.1