# Question

A project consists of three phases to be completed one after the other. The duration of each phase, in days, is normally distributed as follows: Duration of Phase I ~ N(84, 32); Duration of Phase II ~ N(102, 42); Duration of Phase III ~ N(62, 22). The durations are independent.

a. Find the distribution of the project duration. Report the mean and the standard deviation.

b. If the project duration exceeds 250 days, a penalty will be assessed. What is the probability that the project will be completed within 250 days?

c. If the project is completed within 240 days, a bonus will be earned. What is the probability that the project will be completed within 240 days?

a. Find the distribution of the project duration. Report the mean and the standard deviation.

b. If the project duration exceeds 250 days, a penalty will be assessed. What is the probability that the project will be completed within 250 days?

c. If the project is completed within 240 days, a bonus will be earned. What is the probability that the project will be completed within 240 days?

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