Question

In: Statistics and Probability

Ocean fishing for bill fish is very popular in the Cozumel region of Mexico. In the...

Ocean fishing for bill fish is very popular in the Cozumel region of Mexico. In the Cozumel region about 45% of strikes (while trolling) resulted in a catch. Suppose that on a given day a fleet of fishing boats got a total of 29 strikes. Find the following probabilities. (Round your answers to four decimal places.)

(a) 12 or fewer fish were caught

(b) 5 or more fish were caught

(c) between 5 and 12 fish were caught

Expert Solution

Given

n = total number of strikes = 29

p = probability of strikes resulted in a catch = probability of success = 45% = 0.45

x = number of fish caught = number of success

we can find the probability using binomial probability formula and is given by

a)

where, ( Correct upto 4 decimal place )

Now

=

Therefore, the probability that 12 or fewer fish were caught is 0.4213

b)

Therefore, the probability that 5 or more fish were caught is 0.9996

c)

where

and

Now

= 0.4196 +0.0013

= 0.4209

Therefore, the probability that between 5 and 12 fish were caught is 0.4209

orchestra answered 2 years ago

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