Question

In: Math

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then...

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

1313

per day. The port has facilities to handle up to

1717

oil tankers in a day. Find the probability that on a given​ day, (a)

thirteenthirteen

oil tankers will​ arrive, (b) at most three oil tankers will​ arrive, and​ (c) too many oil tankers will arrive.

Solutions

Expert Solution

Let X is a random variable shows the number of tankers arrive per day. It is given that average number of tankers arrive per day is 13 so here X will have Poisson distribution with parameter .

The pdf of X is

(a)

The probability that on a given​ day thirteen oil tankers will​ arrive is

Excel function used to find the probability is ; "=POISSON(13,13,FALSE)"

Answer: 0.1099

(b)

The probability that at most three oil tankers will​ arrive is

Excel function used to find the probability is ; "=POISSON(3,13,TRIE)"

Answer: 0.0011

(c)

Too many oil tankers will arrive means more than 17 tankers will arrive.

The probability that too many oil tankers will arrive is

Excel function used to find the probability is ; "=1-POISSON(17,13,TRUE)"

Answer: 0.1095

milcah answered 6 months ago
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