MDonald ? has nany restaurants around the country. The local denand for apple pies obviously varies a bit ?let? assume that the chenand (innumbers of apple pies) Xis mmally distributed with nean ?X=1000 andstandard deviation X=100. For some logistical reason, MiDonald? must buy exactly the same number Mof apple pies for each of their stores, meaning that a stare can never sel more than Mpies regardless of howlarge the danand Xis, and that a store must always pay for Mpies evenif they sell fewer than that. Your jobis to figure at what the quinal value of Mis, i.e., hownanypies to buy for each stare. The apple pies sell for $0.90 but cost MiDonald ? $0.15 thus the profit Yfor a restaurant is Y=0.90nin (X M 0.15M (a) For the case of M=1060, use N=1000 samples to compute an estimated Boconfidence interval on the expected profit ?Y. (b) For the case of M=1050, howmany samples Nare ineeded to get the Boconfidence interval on ?Yto within ?$1? (c) If you want to maximize the expected profit F(Y) = i.e, the nean profit across all stores, what is the optinal value of MP Hit: For any value of Muse sampling on X And then you can repeat this far different Mvalues ?maybe Pay of MValues