1. The Federal Funds rate in spring 2007 was approximately normal with µ = 5.25% and cr = 0.05%. Find the probability that the rate on a given day will be less than 1.1%.13

2. Thirty-year ?xed mortgage rates in April 2007 seemed normally distributed with mean 6.17%.14 The standard deviation is believed to be 0.25%. Find a bound such that the probability that the actual rate obtained will be this number or below it is 90%.

3. 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?