Please help with Question 5. 5. Y2016) dt Cafi selis verage of su burgers and 10

Question

Please help with Question 5. 5. Y2016) dt Cafi selis verage of su burgers and 100 hotdogs each day. Furthermore, the standard deviation of daily burger and hotdog sales are 4 and 9, respectively. Assume that daily burger and hotdog sales are normally distributed. a) What is the probability that Carl will sell at least 48 burgers in a given day? b) What is the probability that Carl will sell at most 110 hotdogs in a given day? c) What is the probability that total sales in a given day is at least 155? d) What assumption did you have to make in answering the questions above? 6. [Y2015] Consider a factory floor with the following work center layout Entrance Exit Suppose that the flow rate between the work center (WC) is as follows: WC2 30 20 WC3 Exit WC1 50 Enter WC1 WC2 WC3 30 20 20 30 40 Determine the number of different possible work center layouts for this factory. Determine the optimal work center layout for the factory floor a. b.

Explanation / Answer

Formula: Z = (X-mean)/SD

a) P(X >= 48) = P(Z >= (48-50)/4) = P(Z > -0.5) = 0.6915

b) P(Y <= 110) = P(Z <= (110-100)/9) = P(Z<= 1.1111) = 0.8667

c) For sum of normal random variables, mean = 50+100 = 150, SD =sqrt(var1 + var2) = sqrt(4^2 + 9^2) = 9.848858

P(X+Y >= 155) = P(Z >= (155 - 150)/9.848858) = P(Z >= 0.50767) = 0.3058

d) For the above question, the assumption is both random variables, i.e burgers and hotdogs are independent variables.

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