MATH SOLVE

3 months ago

Q:
# 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. 0.7500b. 0.1322c. 0.0000d. 0.0213e. none of the above

Accepted Solution

A:

Answer: d. 0.0213Step-by-step explanation:Given : Mean arrival rate [tex]\lambda[/tex] = 16 customers per hour. The Poisson distribution formula is given by :-[tex]P(X=x)=\dfrac{\lambda^x e^{-\lambda}}{x!}[/tex] ,where[tex]\lambda[/tex] 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 :-[tex]P(X=9)=\dfrac{(16)^9 e^{-16}}{9!}\\\\\text{Simplify}\\\\=0.0213110623928\approx0.0213[/tex]Hence, the probability that in the next hour there will be exactly 9 arrivals= 0.0213Therefore , the correct answer is option (d.).