A new project will be declared “successful” if you achieve a market share of 10% or more in the next two years. Your marketing department has considered all possibilities and decided that it expects the product to attain a market share of 12% in this time. However, this number is not certain. The standard deviation is forecast to be 3%, indicating the uncertainty in the 12% forecast as 3 percentage points. You may assume a normal distribution.
a.* Find the probability that the new project is successful.
b. Find the probability that the new project fails.
c. Find the probability that the new project is wildly successful, defined as achieving at least a 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%.