A venture capital outfit - BigV - is considering investing in a pool of start-up companies. The pool has more than 1,000 companies. BigV has been told average 3 year profits forcompanies in this pool is $30 million. But a nay-sayer on the BigV Board claims that infact 3 year profits are only $28 million. If it turns out that profits are this lower value BigV would prefer not to invest. Your job is to develop a plan to help BigV evaluate the Null Hypothesis: 3 year profitaverage is $30 million for start-ups in the pool, and specifically to make sure a large enoughsample is drawn such that if the Alternative Hypothesis: 3 year profit average is $28 millionis correct, the Null is most likely going to be rejected. Preliminary data analysis determines the standard deviation is approximately $8.0 millionfor firms in this pool. Assume this is correct. Also assume all distributions are Normal. Finally, assume a standard 95% Confidence Interval in which the Null is not rejected.

Required:
a. Draw a graph showing how you work this problem.
b. In solving the problem take into account ONLY the probability associated with the Test Statistic falling below the Null Confidence Interval (the direction the alternative lies). This makes the problem easier to solve and is a very accurate approximation to the answer.