Cars arriving for gasoline at a Shell station follow a Poisson distribution with a mean of 1010 per hour. (Enter all answers rounded to at least 3 decimal places.) (a) Determine the probability that over the next hour, only one car will arrive. (b) Compute the probability that in the next 3 hours, more than 29 cars will arrive.

a)

b) For this case the new parameter would be:

And we want to calculate the following probability:

And we can use the complement rule for this case:

And for this case we can use the following excel code in order to find the required probability:

"=1-POISSON.DIST(29,30,TRUE)"

And we got:

Step-by-step explanation:

Part a

Let X the random variable that represent the number of cars arriving for gasoline at Shell station. We know that

The probability mass function for the random variable is given by:

And for this case we want this probability:

Using the probability mass function we got:

Part b

For this case the new parameter would be:

And we want to calculate the following probability:

And we can use the complement rule for this case:

And for this case we can use the following excel code in order to find the required probability:

"=1-POISSON.DIST(29,30,TRUE)"

And we got:

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