Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 9 arrivals?

a. 0.7500

b. 0.1322

c. 0.0000

d. 0.0213

e. none of the above

Respuesta :

Answer:

d. 0.0213

Step-by-step explanation:

If a variable follow a poisson distribution, the probability that x events happens in a specific time is given by:

[tex]P(x)=\frac{e^{-a}*a^{x} }{x!}[/tex]

Where a is the mean number of events that happens in a specific time.

So, in this case, x is equal to 9 arrivals and a is equal to 16 customers per hour. Replacing this values, the probability is:

[tex]P(9)=\frac{e^{-16}*16^{9} }{9!}[/tex]

[tex]P(9)=0.0213[/tex]