The distribution of water fleas (Daphnia) in a given water pond is fairly random and the population density is fairly constant. The average number of water fleas caught by sweeping the water a single time with a standard net is 3.7 individuals. If tomorrow a net will be used once in the pond what is the probability of catching: a) 5 individuals?b) at least 2 individuals?

(a) The probability of catching 5 individuals in the pond is 0.1429.

(b) The probability of catching at least 2 individuals in the pond is 0.8838.

Step-by-step explanation:

Let X = number of water fleas caught by sweeping the water a single time.

The random variable X follows a Poisson distribution with parameter λ = 3.7.

The probability mass function of the Poisson distribution is:

(a)

Compute the value of P (X = 5) as follows:

Thus, the probability of catching 5 individuals in the pond is 0.1429.

(b)

Compute the value of P (X ≥ 2) as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

Thus, the probability of catching at least 2 individuals in the pond is 0.8838.

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