**Problem: Poisson Distribution at Grand Teton National Park**At the Grand Teton National Park, a ranger watches for moose every morning in August. The number of moose has a Poisson distribution with a mean of 1.4. Find the probability that on a randomly selected morning, the number of moose seen is 5.**Calculate:**P(5) = [Input box]**Explanation:**In this scenario, we are dealing with a Poisson distribution, which is often used to model the number of events happening within a fixed interval of time or space. The key parameter of a Poisson distribution is the average rate (mean) λ (lambda), which in this case is 1.4.The formula for calculating the probability of observing k events (in this case, 5 moose) in a Poisson distribution is:\[ P(k) = \frac{e^{-\lambda} \cdot \lambda^k}{k!} \]Where:- \( e \) is the base of natural logarithms (approximately equal to 2.71828),- \( \lambda \) is the mean number of occurrences (1.4 here),- \( k \) is the actual number of occurrences (5 moose here),- \( ! \) denotes factorial, the product of all positive integers up to that number.

Name: **Problem: Poisson Distribution at Grand Teton National Park**At the
Uploaded: 2024-03-20T07:06:41.000Z
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Description: **Problem: Poisson Distribution at Grand Teton National Park**At the Grand Teton National Park, a ranger watches for moose every morning in August. The number of moose has a Poisson distribution with a mean of 1.4. Find the probability that on a ran