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?