For the market share model in Problem 5 of Chapter 11, 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%. Conduct a Monte Carlo simulation with 250 trials and compute summary statistics of the long-run market share.

Data from problem 5 chapter 11

A company is trying to predict the long-run market share of a new men's deodorant.¹⁰ Based on initial marketing studies, they believe that 35% of new purchasers in this market will ultimately try this brand, and of these, about 60% will purchase it 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.