Question

Question 3 (10 points) You've invited 100 guests to a dinner party where the only item on the menu are shawarma sandwiches! Let X; (where 1<i< 100 denote the number of shawarma sandwiches the i-th guest consumes at the party. Suppose you believe that X; = 0,1, or 2 with probability 1/10,8/10, and 1/10 respectively (for 1<i<100). Suppose you also believe that the number of shawarma sandwiches each guest consumes is independent from the number of shawarma sandwiches other guests consume. Use the Central Limit Theorem to determine how many shawarma sandwiches you should order to be 95% sure there is no shortage (with no whole shawarma sandwiches wasted of course).

Answer 1

Q. M: Exipi= on ito + 1x 8 6 + 2x 40 = 1.0 & E(X)= Ex?P₂ = 8 to 2 x + ²x + 0 2102 o= 11.2-(132 a 50.2 for a sample of 100 guest, se = 100 - 10.2/100 = 50.002 Let X be the no of sandwiches required, P(X=x) = 0.3s > P(x<= 0.45 - Plzs X-100 -0.95 0.05 10.002 1.69 ...2= 100.07 - 101) - x x CZ-1.645) (:P(Z 51.645)-0.95)