Question

Assume that BK Call Center receives 2 phone calls in one hour on average. If the department works 10 hours a day receiving the class, find the probability,
A. Exactly 20 calls will be received at a particular day
B. No call is received in a particular hour
C. At least 1 call will be received in a particular hour

Answer 1

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%.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

• x is the number of successes

• e = 2.71828 is the Euler number

• $\mu$ is the mean in the given interval.

Item a:

10 hours, 2 calls per hour, hence the mean is given by:

$\mu = 2 \times 10 = 20$.

The probability is P(X = 20), hence:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 20) = \frac{e^{-20}20^{20}}{(20)!} = 0.0888$

Item b:

1 hour, hence the mean is given by:

$\mu = 2$

The probability is P(X = 0), hence:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-2}2^{0}}{(0)!} = 0.1354$

Item c:

The probability is:

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1354 = 0.8646$

More can be learned about the Poisson distribution at brainly.com/question/13971530

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