A website receives an average of 200 visitors per hour. What is the probability that the website will receive more than 220 visitors in the next hour?

To answer this question, we need to use the concept of Poisson distribution, which is a probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space.

However, to calculate the exact probability of getting more than 220 visitors in the next hour, we need to know the standard deviation or the variance of the distribution, which is not provided in the question.

In a Poisson distribution, the mean is equal to the variance. So if we assume that the distribution of visitors is Poisson, then the variance is also 200. The standard deviation would be the square root of the variance, which is approximately 14.14.

We can then convert 220 to a z-score, which is a measure of how many standard deviations an element is from the mean. The formula for the z-score is (X - μ) / σ, where X is the number of visitors (220), μ is the mean number of visitors (200), and σ is the standard deviation (14.14).

The z-score would be (220 - 200) / 14.14 = 1.41 approximately.

We can then look up this z-score in a standard normal distribution table, or use a calculator or software that can do this. The area to the left of 1.41 in the standard normal distribution is approximately 0.921.

However, we want the probability of getting MORE than 220 visitors, so we need to subtract this from 1 to get the area to the right of 1.41.

So, the probability of getting more than 220 visitors in the next hour is approximately 1 - 0.921 = 0.079 or 7.9%.

Please note that this is an approximation based on the assumption that the distribution of visitors follows a Poisson distribution and that the variance is equal to the mean. The actual probability may be different if these assumptions are not accurate.