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 8 per day. The port has facilities to handle up to 10 oil tankers in a day. Find the probability that on a given​ day, (a) eight oil tankers will​ arrive, (b) at most three oil tankers will​ arrive, and​ (c) too many oil tankers will arrive. ​(a) ​P(eight oil tankers will ​arrive)equals . 1395 ​(Round to four decimal places as​ needed.) ​(b) P(at most three oil tankers will ​arive)equals . 0424 ​(Round to four decimal places as​ needed.) ​(c) P(too many oil tankers will ​arrive)  ​(Round to four decimal places as​ needed.) Need the answer for problem "C"

Answer 1

This questions is a case of Poisson distribution as we are interested in the no. of successes over a period of time.

C.

We know that,

= 8

Let X be the random variable which denotes the no. of success in the one-day interval.

P(X = x) =

As per the question, the port's capacity is to handle up to 10 tankers a day so too many tankers' arrivals would mean tankers > 10.

Thus,

P(too many oil tankers will arrive) = P(X>10) = 1 - P(X10)

= 1 -

= 1 - 0.81589

= 0.18411

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