A new project will be declared "successful" if you attain a market share of 10% or more in the next two years. Your marketing department has considered all possibilities as well as decided that it expects the product to attain market share of 12% in this time. But, this number is not certain. The standard deviation is forecast to be 3% indicating the uncertainty in 12% forecast as 3 percentage points. You may assume a normal distribution.
a. Determine the probability that the new project is successful.
b. Determine the probability that the new project fail.
c. Determine the probability that the new project is wildly successful, defined as achieving at least 15% market share.
d. To assess the precision of the marketing projections, find the probability that the attained market share falls close to the projected value of 12%, that is, between 11% and 13%.