he demand for a product varies frugm msnth to month Based on the past year\'s da
ID: 3365690 • Letter: H
Question
he demand for a product varies frugm msnth to month Based on the past year's data, the LT Variables (Chapters 4-6) ollowing probability distribution shows MNM Compary 's monthly damand. 122 peiats) d. What is the probability that the monthly demand equals O units? PN) Unit Demand Probability e. What is the probability that the monthly demand is at ost 2000 units 0.10 0.40 0,30 f. Determine the expocted number of units demanded per month 4,000 E What is the variance for the number of units demanded per month? a. What is the random variable? h. What is the standard deviation for the sumber of units demanded per mooth? b. What is the probability that monhly demand is between 1,000 and 3000 units inclusive? L Each unit roduced costs the company $8.00, What is the cost to the company if it stocks the expocted namber of units? c. What is the probability that the monthly demand exceeds 3000 units? j Each unit prodaced is sold for $10.00. What is the revenue that is gonenated if the company soll only 2000 units? How much will the company gain or lose in a moath in this scemario? Hint: Profit - Revenue-Costs) k.Explanation / Answer
(a) The demand for a product is a random variable i.e. X (unit demand) as it carries some porbability of occurence
(b)P(1000<=X<=3000) = P(X=1000)+(X=2000)+P(X=3000) = 0.40+0.30+0.15 = 0.85
(c) P(X>3000) = P(X=4000) = 0.05
(d) P(X=0) = 0.10
(e) P(X<=2000) = P(X=0)+P(X=1000)+P(X=2000) = 0.10+0.40+0.30 = 0.80
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