It is known that, on average, a predatory

Col phiperr

Col phiperr

Answered question

2022-07-05

It is known that, on average, a predatory fish catches 1 prey in 10 minutes. Find the
probability that the fish will catch 8 preys in an hour.

Answer & Explanation

xleb123

xleb123

Skilled2023-06-02Added 181 answers

To find the probability that a predatory fish will catch 8 preys in an hour, we can use the Poisson distribution.
The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time, given the average rate at which the events occur.
In this case, the average rate of the fish catching prey is 1 prey in 10 minutes. To find the average rate per hour, we can convert 10 minutes to hours:
1 prey in 10 minutes=16 prey per hour
Let's denote the average rate per hour as λ, which is 16. The probability of the fish catching exactly 8 preys in an hour can be calculated using the Poisson distribution formula:
P(X=k)=eλ·λkk!
where X represents the random variable (number of preys caught), λ represents the average rate, k represents the specific number of preys (8 in this case), and e is Euler's number, approximately 2.71828.
Substituting the values into the formula, we have:
P(X=8)=e16·(16)88!
Calculating this expression will give us the probability that the fish will catch exactly 8 preys in an hour.

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