A new product has the following demand/unit sale price characteristics: Sales Vo
ID: 1207201 • Letter: A
Question
A new product has the following demand/unit sale price characteristics:
Sales Vol. (units)
Prob.
Sale Unit Price $
Prob.
30,000
0.15
3.50
0.15
45,000
0.40
3.00
0.20
50,000
0.30
2.75
0.45
75,000
0.15
2.50
0.20
What are the Estimated Value (Mean) and the Standard Deviation (SD) of the gross income from the sale of this product.
What is the probability that the gross income will be more than $170,000?
Sales Vol. (units)
Prob.
Sale Unit Price $
Prob.
30,000
0.15
3.50
0.15
45,000
0.40
3.00
0.20
50,000
0.30
2.75
0.45
75,000
0.15
2.50
0.20
Explanation / Answer
Answer.
Probability(Total income)
{Average of probability of quantity and price)
P*(Xi -Ex)2
(Variance)
Where Xi is income
Estimated Value = $140,625
Variance = $588,046,875
Standard deviation = (Variance)1/2 = (588,046,875)1/2 = $24249.67
The probability that the gross income will be more than $170,000 is 0.175
Sale Volume (Quantity) Prob (Quantity) Price ($) Probability (Price$) Total Income (Quantity*Price)Probability(Total income)
{Average of probability of quantity and price)
P*Total Income {Estimated Value i.e mean (Ex)}P*(Xi -Ex)2
(Variance)
Where Xi is income
30,000 0.15 3.50 0.15 105,000 0.15 15,750 190,371,093.75 45,000 0.40 3.00 0.20 135,000 0.30 40,500 9,492,187.5 50,000 0.30 2.75 0.45 137,500 0.375 51,562.5 3,662,109.375 75,000 0.15 2.50 0.20 187,500 0.175 32,812.5 384,521,484.375 = 1 = 1 = 1 = $140,625 = $588,046,875Related Questions
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