Quantitative Method of Business Chapter 3 Answer

BUS501 answers to homework of ch 3 1. The Demand for a product of Carolina Industries varies greatly from month to month. Based on the past two years’ data, the following probability distribution shows the company’s monthly demand. Unit Demand Probability 300 0.20 400 0.35 500 0.30 600 0.15 a. If the company places monthly orders equal to the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product? b. Assume that each unit demanded generates $70 in revenue and that each unit ordered costs $57. How much will the company gain or lose in a month if it places an order based on your answer to part (a) if the actual demand for the item is 320 units? c. What is the variance and the standard deviation for the number of units demanded?

Ans: a. E(x)= ∑xif (xi) = 300(0.20) + 400(0.35) + 500(0.30) + 600(0.15) = 440 The monthly order quantity should be 440 units. b. Cost: Revenue: c. x 300 400 500 600 f (x) 0.20 0.35 0.30 0.15 µ= x*f(x) 60.00 140.00 150.00 90.00 440.00 (x - u) -140.00 -40.00 60.00 160.00 (x - u)^2 19600.00 1600.00 3600.00 25600.00 var. = σ= (x - u)^2*f (x) 3920 560 1080 3840 9400 96.95 440 @ $57 = $25,080 320 @ $70 = $22,400 22,400 – 25,080 = – $ 2,680 Loss

2. In a Youth and Money Survey, sponsored by the American Savings Education council, the Employee Benefit Research Institute, and the Mathew Greenwald & Associates, talked to 900 students ages 16-20 about personal finance. The Survey found that 45% of the students have their own credit card. a. In a sample of five students, what is the probability that two will have their own credit card? b. In the sample of six students, what is the probability that at least two will have their own credit card? c. In the sample of 10 students, what is the probability that at none will have their own credit card?

Ans: a. b. c. f(2) = {5! / [2!×(5-2)!]} p2 (1 – p)(5-2) = {120/[2×6]} ×0.452×0.553 = 0.337 P(at least 2) = 1 - f(0) - f(1) = 1 – {6!/[0! × (6-0)!]} × p0 (1 – p)(6-0)...