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) = 0.1144
(round to four decimal places as needed.)

(b) p(at most three oil tankers will arrive) = 0.0023
(round to four decimal places as needed.)

(c) p(too many oil tankers will arrive) = 0.1556
(round to four decimal places as needed.)

a. the event in part (a) is unusual.
b. the event in part (b) is unusual.
c. the event in part (c) is unusual.
d. none of the events are unusual.

Explanation:

Identify the distribution parameters and event probabilities

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Determine which events are unusual

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Select the correct multiple-choice option

$$ \text{Only the event in part (b) is unusual, which corresponds to option B.} $$

Answer:

• A. The event in part (a) is unusual.
• B. The event in part (b) is unusual. (Correct answer)
• C. The event in part (c) is unusual.
• D. None of the events are unusual.