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An average of 2 customers per minute arrive at a local amusement park. What is the probability that exactly 4 customers arrive in the next 2 minutes?

A. 32.1%
B. 100%
C. 50%
D. 10.1%
E. 19.5%
F. 6.2%
G. 23.6%

User Spikes
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1 Answer

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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.

User Dshepherd
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