Answer:
13.77% probability that exactly seven customers enter the queue in a randomly selected 15-minute period
Step-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 which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
A bank manager estimates that an average of two customers enters the tellers' queue every five minutes.
We are working in a fifteen minutes interval, so [tex]\mu = \frac{15*2}{5} = 6[/tex]
What is the probability that exactly seven customers enter the queue in a randomly selected 15-minute period
This is P(X = 7).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 7) = \frac{e^{-6}*(6)^{7}}{(7)!} = 0.1377[/tex]
13.77% probability that exactly seven customers enter the queue in a randomly selected 15-minute period
