Question

The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ=9. ​(a) Compute the probability that more than 16 customers will arrive in a 2-hour period.​ (b) What is the mean number of arrivals during a 2-hour period?

​(a) The probability that more than 16 customers will arrive is

​(Round to four decimal places as​ needed.)

​(b) The mean number of arrivals is

​(Type an integer or a decimal. Do not​ round.)

Answer 1

(a)

Let X denote the random variable representing the number of customers arriving in a 2 hour period.

Now, we are given that the number of customers arriving per hour at the automobile service facility is assumed to follow a Poisson distribution with mean λ=9. Thus, we can conclude that the number of customers arriving in a 2 hour period at the automobile service facility is a Poisson distribution with mean 18.

Thus, X ~ Poisson(18)

Now, the probability that more than 16 customers will arrive in a 2-hour period is given by:

(b)

We know that E(Poisson()) =

Now, we know that X ~ Poisson(18)

=> E(X) = E(Poisson(18)) = 18

=> Mean number of arrivals during a 2-hour period = 18 [ANSWER]

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