module 10.pdf

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Ryerson University
Quantitative Methods
QMS 102
Changping Wang

8/4/2014… QMS102 Winter 2014 Module 10 Questions for Nabil Score:89% 1. The lifetime ofa certain brand oftire is normally distributed with a mean of100,000 km. and standard deviation of11,000 km. The tire carries a warranty for 80,000 km. a) What is the probability that the tire you recently purchased willlast at least 101,000 km.0.4638 Soln: 0.4638 Eval: 1/1 b) What percent ofthis brand oftire willfailbefore the warranty expires? 3.45 % format{~.dd} Soln: 3.45 Eval: 1/1 c) What should the mileage warranty be so that only 2% ofthe tires need to be replaced under warranty? 122591 km. format{ w} Soln: 77409 Eval: 0/1 Feedback: IDF.NORMAL(0.02, 100000, 11000) 2. A firm's marketing manager believes that totalsales for next year can be represented by a normaldistribution, with a mean of$2.4 million and a standard deviation of$400,000. The firmhas fixed costs of$1.6 million. a) What is the probability that the firm's sales willbe less than $3.3 milli0.9878 Soln: 0.9878 Eval: 1/1 b) What is the probability that the firmwillhave sufficient sales to cover fixed cost0.9772 Soln: 0.9772 Eval: 1/1 c) What is the probability that the firm's sales willbe within $150,000 ofthe expected sales?0.2923 Soln: 0.2923 Eval: 1/1 d) Determine the sales levelthat has only a 7% chance ofbeing exceeded. $ 2.99 million.format{~.dd} Soln: 2.99 Eval: 1/1 3. The owner ofa convenience store has copies ofthe localnewspaper delivered early each morning. The demand for papers is normally distributed with a mean of72 and a standard deviation of18. {Assume daily demand is continuous} a) What is the probability that there willnot be enough newspapers to meet demand ifthe owner orders 70 copies? 0.5442 Soln: 0.5442 Eval: 1/1 b) How many copies should be ordered so that the probability of"selling out"is at most 13% ? 92.28 papers.… 8/4/201… Soln: 93 Eval: 0/1 Feedback: ROUNDUP[IDF.NORMAL(1-.13, 72, 18)] 4. An investment broker reports that the annualreturns on common stock and municipalbonds are both no
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