The demand for a product of Carolina Industries varies greatly from month to mon

Question

The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand.

(a) If the company bases monthly orders on the expected value of the monthly demand, what should Carolina’s monthly order quantity be for this product?

(b) What is the variance of the monthly demand for this product?

(c) What is the probability that the monthly demand is at least 500?

(d) What is the probability that the monthly demand will be less than 400?

(e) What is the probability that the monthly demand is at most 400?

Monthly Demand Probability 300 0.20 400 0.30 500 0.35 600 0.15

Explanation / Answer

a)

Expected monthly demand = 300*0.2 + 400*0.3 + 500*0.35 + 600*0.15 =445

b)

c)

P(D>=500) = 0.35+0.15 = 0.50

d)

P(D<400) = 0.20

e)

P(D<=400) = 0.20+0.30 = 0.50

Monthly Demand Probability D*P D - Mean (D-Mean)^2 P*(D-Mean)^2 300 0.2 60 -145 21025 4205 400 0.3 120 -45 2025 608 500 0.35 175 55 3025 1059 600 0.15 90 155 24025 3604 Mean = 445 Variance= 9475

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