A company is trying to predict the long-run market share of a new men's deodorant.8 Based on initial marketing studies, they believe that 35% of new purchasers in this market will ultimately try this brand. They believe that customers will purchase their brand about 60% of the time in the future. Preliminary data also suggest that the brand will attract heavier-than-average buyers, such as those who exercise frequently and participate in sports, and that they will purchase about 20% more than the average buyer. 8 Based on an example of the Parfitt-Collins model in Gary L. Lilien, Philip Kotler, and K. Sridhar Moorthy, Marketing Models (Englewood Cliffs, NJ: Prentice Hall, 1992): 483. Calculate the long-run market share that the company can anticipate under these assumptions. Develop a general model for predicting long-run market share.

For the market share model in the above Problem, suppose that the estimate of the percentage of new purchasers who will ultimately try the brand is uncertain and assumed to be normally distributed with a mean of 35% and a standard deviation of 4%. Use the NORM.INV function and a one-way data table to conduct a Monte Carlo simulation with 25 trials to find the distribution of the long-run market share.