Respuesta :
Answer:
There is a 14.65% probability that during a randomly selected half-hour period, exactly 2 customers use the service desk.
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
[tex]e = 2.71828[/tex] is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour.
This means that [tex]\mu = 4[/tex]
What is the probability that during a randomly selected half-hour period, exactly 2 customers use the service desk?
This is P(X = 2). So
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 2) = \frac{e^{-4}*(4)^{2}}{(2)!} = 0.1465[/tex]
There is a 14.65% probability that during a randomly selected half-hour period, exactly 2 customers use the service desk.
