Question

a service center receives an average of 0.7 customer complaints per hour. management's goal is to receive fewer than three complaints each hour. assume the number of complaints follows the poisson distribution. determine the probability that exactly four complaints will be received during the next eight hours.

Answer 1

The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by $P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}$ where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

$\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}$

The required answer is 15.41%.

To know more about Poisson distribution:

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