Now, to explain how the Poisson distribution can approximate the binomial distribution. Say that we would want to know the probability of exactly 3 visitors arriving at the art gallery in each hour. 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 does this represents how the Poisson distribution can appximate the binomial distribution