QUESTION 13 - 1 POINT Ruby has a bird feeder which is visited by an average of 13 birds every 2 hours during daylight hours. What is the probability that the bird feeder will be visited by more than 3 birds in a 40 minute period during daylight hours? - Round your answer to three decimal places. Provide your answer below:

Step 1 ：The problem is asking for the probability of more than 3 birds visiting the bird feeder in a 40 minute period. We know that on average, 13 birds visit the bird feeder every 2 hours (or 120 minutes).

Step 2 ：First, we need to find the average number of birds that visit the bird feeder in 40 minutes. We can do this by setting up a proportion: \(\frac{13 \text{ birds}}{120 \text{ minutes}} = \frac{x \text{ birds}}{40 \text{ minutes}}\). Solving for x will give us the average number of birds that visit the bird feeder in 40 minutes, which is approximately \(4.33\).

Step 3 ：Next, we need to calculate the probability of more than 3 birds visiting the bird feeder in a 40 minute period. This is a Poisson distribution problem, where the Poisson distribution is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

Step 4 ：The formula for the Poisson distribution is: \(P(x; \mu) = \frac{e^{-\mu} * (\mu^x)}{x!}\), where: \(P(x; \mu)\) is the Poisson probability, which asks the question 'what is the probability that exactly x events happen when the average rate of success is \(\mu\)?', \(e\) is the base of the natural logarithm, approximately equal to 2.71828, \(\mu\) is the average rate of success, which in this case is the average number of birds that visit the bird feeder in 40 minutes, and \(x\) is the actual number of successes that result from the experiment, which in this case is the number of birds that visit the bird feeder in a 40 minute period.

Step 5 ：Since we want the probability of more than 3 birds visiting the bird feeder in a 40 minute period, we need to calculate \(1 - P(0; \mu) - P(1; \mu) - P(2; \mu) - P(3; \mu)\).

Step 6 ：Finally, we need to round our answer to three decimal places. The probability that the bird feeder will be visited by more than 3 birds in a 40 minute period during daylight hours is \(\boxed{0.629}\).