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

Explanation:

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

The Poisson distribution formula is given by :-

`P(X=x)=(\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)=((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.).