Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities.

the mean number of oil tankers at a port city is 12 per day. the port has facilities to handle up to 15 oil tankers in a day. find the probability that on a given day, (a) twelve oil tankers will arrive, (b) at most three oil tankers will arrive, and (c) too many oil tankers will arrive.

(a) p(twelve oil tankers will arrive) =
(round to four decimal places as needed.)

Explanation:

Identify the distribution parameters

$$ \lambda = 12,\quad x = 12 $$

Apply the Poisson probability formula

$$ P(X = 12) = \frac{e^{-12} \cdot 12^{12}}{12!} $$

Calculate the numerical value

$$
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$$

Answer:

(a) P(twelve oil tankers will arrive) = <blank>0.1144</blank>
(Round to four decimal places as needed.)