3) The demand for a product varies from month to month. Based on the past year's data, the following probability distribution shows MNM company's monthly demand.
x |
f(x) |
Unit Demand |
Probability |
0 |
.10 |
1,000 |
.10 |
2,000 |
.30 |
3,000 |
.40 |
4,000 |
.10 |
a. Determine the expected number of units demanded per month and the standard deviation
Solution :
x | P(x) | x * P(x) | x^{2} * P(x) |
0 | 0.1 | 0 | 0 |
1000 | 0.1 | 100 | 100000 |
2000 | 0.3 | 600 | 1200000 |
3000 | 0.4 | 1200 | 3600000 |
4000 | 0.1 | 400 | 1600000 |
Sum | 1 | 2300 | 6500000 |
Mean = = X * P(X) = 2300
Expected number of units demanded per month = 2300
Standard deviation =
=X ^{2} * P(X) - ^{2}
= (6500000 - 2300^{2})
= 1100
Standard deviation = 1100
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