Answer :
Answer:
28.65% probability that the next customer will not arrive for 5 minutes
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 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