McDonald's has many restaurants around the country. Their local demand for apple pies obviously varies a bit. Let's assume that the demand (in numbers of apple pies) X is normally distributed with mean ux = 1070 and standard deviation ox = 110. For some logistical reason, McDonald's must buy exactly the same number M of apple pies for each of their stores, meaning that a store can never sell more than M pies regardless of how large the demand X is, and that a store must always pay for M pies even if they sell fewer than that. Your job is to figure out what the optimal value of M is, i.e., how many pies to buy for each store. The apple pies sell for $0.99 but cost McDonald's $0.15, thus the profit Y for a restaurant is: Y = 0.99 min(X, M) 0.15 M. For the case of M = 1060, use N = 1300 samples to compute an estimated 90% confidence interval on the expected profit Hy. Yib = number (rtol=0.1, atol=D0.0001) Yub = number (rtol=0.1, atol=D0.0001) For the case of M = 1040, how many samples N are needed to get the 85% confidence interval on y to within + $1? (Round your answer to the nearest integer) N = number (rtol=0.1, atol=0.001) If you want to maximize the expected profit E(Y) = y, i.e., the mean profit across all stores, what is the optimal value of M? (Hint: For any value of M, use sampling on X. And then you can repeat this for different M values. Maybe use an array of M values. number (rtol=0.05, atol=D0.0001) As the CEO, your annual bonus is based on the profits only at the top 10% of restaurants. You need a new boat, so what value of M maximizes the expected profit among those restaurants (i.e., the average among only the highest 10%)? M = number (rtol=0.05, atol=D0.0001)