Answer :
Answer:
The probability of observing between 9 and 15 (inclusive) swarms is 0.6639.
Step-by-step explanation:
The random variable X can be defined as the number of swarms of honeybees seen each spring.
The average value of the random variable X is, λ = 13.
A random variable representing the occurrence of events in a fixed interval of time is known as Poisson random variables.
For example, the number of customers visiting the bank in an hour or the number of typographical error is a book every 10 pages.
So, the random variable X follows a Poisson distribution with parameter λ = 13.
The probability mass function of X is as follows:
[tex]P(X=x)=\frac{e^{-\lambda}\ \lambda^{x}}{x!}; x=0,1,2,3...[/tex]
Compute the the probability of observing between 9 and 15 (inclusive) swarms as follows:
P (9 ≤ X ≤ 15) = P (X = 9) + P (X = 10) + P (X = 11) + ... + P (X = 15)
[tex]=\sum\limits^{15}_{x=9}{\frac{e^{-\lambda}\ \lambda^{x}}{x!}}\\\\=0.06605+0.08587+0.10148+0.10994\\+0.10994+0.10209+0.08848\\\\=0.66385\\\\\approx 0.6639[/tex]
Thus, the probability of observing between 9 and 15 (inclusive) swarms is 0.6639.