The number of customers coming to a store during regualr work hours has an average of 15 customers/hour and follows a Poisson process. A customer walks in what is the probability that the next customer will not arrice for 5 minutes?

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Question:

The number of customers coming to a store during regualr work hours has an average of 15 customers/hour and follows a Poisson process. A customer walks in what is the probability that the next customer will not arrice for 5 minutes?

Answer:28.65% probability that the next customer will not arrive for 5 minutesStep-by-step explanation:In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]In whichx is the number of sucessese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given time interval.Mean of 15 customers an hour:An hour has 60 minutes, so in the space of 5 minutes, the mean is:[tex]\mu = \frac{15*5}{60} = 1.25[/tex]A customer walks in what is the probability that the next customer will not arrive for 5 minutes?This is P(X = 0).[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex][tex]P(X = 0) = \frac{e^{1.25}*(1.25)^{0}}{(0)!} = 0.2865[/tex]28.65% probability that the next customer will not arrive for 5 minutes

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