. After an analysis of incoming faxes, the manager of an accounting firm determined the
probability distribution of the number of pages (X) per facsimile as follows:
X 1 2 3 4 5 6 7
P(x) 0.05 0.12 0.20 0.30 0.15 0.10 0.08
Calculate the mean and variance of the number of pages per fax. Further analysis by manager
revealed that the cost of processing each page of a fax is $0.25. Determine the mean and variance
of cost per fax.
Answers
Given : probability distribution of the number of pages (X)
X 1 2 3 4 5 6 7
P(x) 0.05 0.12 0.20 0.30 0.15 0.10 0.08
To Find : mean and variance of the number of pages per fax.
Determine the mean and variance of cost per fax.
Solution:
X P(x) XP(X) X²P(X)
1 0.05 0.05 0.05
2 0.12 0.24 0.48
3 0.2 0.6 1.8
4 0.3 1.2 4.8
5 0.15 0.75 3.75
6 0.1 0.6 3.6
7 0.08 0.56 3.92
1 4 18.4
Mean = ∑X(P(X) = 4
mean of the number of pages per fax = 4
cost of processing each page of a fax is $0.25.
mean of cost per fax. = 4 * 0.25 = 1 $
Variance = ∑X²P(X) - (∑X(P(X))² = 18.4 - 4²
= 18.4 - 16
= 2.4
variance of the number of pages per fax = 2.4
cost of processing each page of a fax is $0.25.
variance of cost per fax. = 2.4 * 0.25 = 0.6 $
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