A new project will be declared successful if you achieve a m

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 nenw project is successful.

b. Find the probability that the new project fail.

c. Find 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%.

Solution

They like to confuse you with percentages and percentage points. Percentages are relative, where as percentage points are absolute.
e.g. percentage change from 10% to 12% is 20% ((12-10)/10 = 0.2 or 20%)
the change in percentage points from 10% to 12% is 2% (12-10 = 2)

Using:
(X-mean)/standard deviation to find the probably on the standard normal distribution:
(10-12)/3 = -2/3 = -0.6666 <-the standard deviation always use absolute values
In the Z tables, it shows that under z>-0.66, there is an area of 0.2546 under the standard normal distribution curve.

This means there is a 25.46% (not percentage points) chance that the project is going to do a belly up