Answer:
The probability of the number of starfish dropping below 3 is 0.0463.
Step-by-step explanation:
Let X represent the number of starfish in the tide pool.
X follows a Poisson distribution with mean 6.4.
The formula for Poisson distribution is as follows.
[tex]P(X=x) = e^{-6.4} * [6.4^{x} / x!] when x = 0, 1, ...[/tex]
[tex]P(X = x) = 0[/tex] otherwise
We need to find the probability that the number of starfish in the tide pool drops below 3.
Therefore, the required probability is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X=2)
[tex]P(X < 3) = e^{-6.4} + (e^{-6.4}*6.4) + (e^{-6.4}*6.4^{2}/2)[/tex]
P(X < 3) = 0.00166 + 0.01063 + 0.03403
P (X < 3) = 0.0463
