Final answer:
To find the probability that exactly 4 customers arrive in the next 2 minutes at a local amusement park with an average rate of 2 customers per minute, we can use the Poisson distribution with a mean of 4 customers. Plugging in the values, we find that the probability is 4.89%.
Step-by-step explanation:
To solve this problem, we can use the Poisson distribution. The Poisson distribution can be used to model the number of events that occur within a specified period of time, given the average rate of events.
In this case, we know that the average rate of customers arriving is 2 per minute. The number of events that occur in a given time period follows a Poisson distribution with a mean equal to the average rate times the length of the period. So, the mean is 2 customers per minute * 2 minutes = 4 customers.
The formula for the probability mass function of the Poisson distribution is P(X=k) = (e^-λ * λ^k) / k!, where X is the number of events, λ is the mean, and k is the number of events we're interested in.
Therefore, to find the probability that exactly 4 customers arrive in the next 2 minutes, we can plug in λ=4 and k=4 into the formula:
- P(X=4) = (e^-4 * 4^4) / 4! = 0.0733 * 16 / 24 = 0.0489 = 4.89%
So, the correct answer is 4.89%, which is not one of the options listed.