Using the Poisson distribution, the probabilities are given as follows:
A. 0.0888 = 8.88%.
B. 0.1354 = 13.54%.
C. 0.8646 = 86.46%.
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
Item a:
10 hours, 2 calls per hour, hence the mean is given by:
[tex]\mu = 2 \times 10 = 20[/tex].
The probability is P(X = 20), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 20) = \frac{e^{-20}20^{20}}{(20)!} = 0.0888[/tex]
Item b:
1 hour, hence the mean is given by:
[tex]\mu = 2[/tex]
The probability is P(X = 0), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1354[/tex]
Item c:
The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1354 = 0.8646[/tex]
More can be learned about the Poisson distribution at https://brainly.com/question/13971530
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