DA01704 & DAO1704X & DSC1007 & DSC1007X b. Tony is a technopreneur who has started up a company called Infinity Technologies that manufactures "smart" wearables. Its main product line is code-named the GauntletTM, a type of smart glove, which would be ready for sale in October 2020. Tony estimated that demand for the Gauntlet in the month of October 2020 would be well- approximated by a normal distribution having a mean of 1,000 units and standard deviation of 200 units. In the month of October 2020, what is the probability that the demand for Gauntlets TM. Exceeds 1,300 units? (1 marks) =1 - NORM.DIST(1300, 1000, 200, TRUE) = 0.0668 ii) Either falls below 800 units or exceeds 1,100 units? (2 marks) =NORM.DIST(800, 1000, 200, 1) + 1 - NORM.DIST(1100, 1000, 200, 1) = 0.467 A private equity firm, Snap Equities, intends to make a big investment in Infinity Technologies, but will only do so if demand for the Gauntlet M exceeds 1,200 units per month for at least two out of the three months of October, November, and December 2020. Assume that the demand for Gauntlet M in October, November and December 2020 are all identical in distribution and independent of each other. iii) What is the probability that Snap Equities makes this investment? (3 marks) p = 1 - NORM.DIST(1200, 1000, 200, 1) Answer = 1 - BINOM.DIST(1, 3, p, 1) = 0.06755 DAO1704 & DAO1704X & DSC1007 & DSC1007X Tony realizes that in order for each GauntletTM to function properly, he requires 6 identical Gyroscopic Electro-Magnetic Systems (G.E.M.S.) to be installed per Gauntlet. Stephen is the sole supplier of G.E.M.S., and can supply as many G.E.M.S. as Tony needs. Let Y be a random variable that represents the total number of G.E.M.S. supplied by Stephen to Tony for the months of October, November, and December 2020 combined. iv) What is the mean of Y? (2 marks) Let X1, X2, X3 be monthly demands for Gauntlets in the respective months of October, November, and December 2020. Then, Y = 6(X1 + X2+ X3) = Y ~ N(18000, 1200V3) So, E(Y) = 18000 v) What is the standard deviation of Y? (3 marks) S.D.(Y) = 1200 * SQRT(3) = 2,078