Question

Suppose your company wanted to determine the amount of sales of a new SUV model, called Lightning. The sales estimate would be based on the overall demand of various SUV model types. Overall demand is assumed to be normally distributed with a mean of 3 million units and standard deviation of 500,000 units. The share of demand that Lightning will take is assumed to be 4%. After running 1,000 simulated scenarios, a 95% confidence interval was constructed for the expected sales of Lightning units sold with limits of 93,048 and 146,964.

1. If 1,000 new simulated scenarios were run, would you get the exact result? Explain why.
2. Would the results be more stable if you ran 2,000 runs? Explain why.
3. Is there a number of simulations that can be run so that the results do not change if you re-ran the simulations? Explain.

Answer 1

a. No, we would get different answer with slight change. Since everytime it takes different (random) samples, therefore, the result has changed slightly.

b. Yes, if we run 2000 times, we would get more stable result than previous one. Because here we are using 1000 more samples. As we increase the number of samples, we are going to get the exact result.

c. Yes, if we simulate these data more than 100000 times, we get exact result. If we still find a slight difference, then we should imcrease this number to get the same result. If we keep increasing this number, then surely at some certain value, we will get the same number.