Question

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

Answer 1

Answer: d. 0.0213

Step-by-step explanation:

Given : Mean arrival rate $\lambda$ = 16 customers per hour.

The Poisson distribution formula is given by :-

$P(X=x)=\dfrac{\lambda^x e^{-\lambda}}{x!}$ ,where$\lambda$ is the mean of the distribution.

If X = the number of customers arrivals , then the probability  that in the next hour there will be exactly 9 arrivals will be :-

$P(X=9)=\dfrac{(16)^9 e^{-16}}{9!}\\\\\text{Simplify}\\\\=0.0213110623928\approx0.0213$

Hence, the probability that in the next hour there will be exactly 9 arrivals= 0.0213

Therefore , the correct answer is option (d.).