The Poisson distribution can be used to predict the probability of a certain number of visitors to the art gallery in a day, given the average rate of 50 visitors per day. Now, to explain how the Poisson distribution can approximate the binomial distribution. Based on previous data, the gallery would have 50 visitors a day. Should the gallery be open for 10 hours per day, the average visitor number per hour would be 5. Binomial Distribution Approach: Number of trials (n) = total visitors per day = 50 Probability of success (p) = 1/10 (the chance that a visitor arrives at a specific hour) Poisson distribution can approximate the binomial distribution when: - The number of trials (n) is large - The probability of success (p) is small - The product of the number of trials and the probability of success (np) is moderate With the above approach: Number of trials (n): 50 (total number of visitors per day) Probability of success (p): 1/10 = 0.1 (this is the probability of a visitor arriving in a specific hour) np = 50 x 0.1 = 5