Here's my previous example: At a theme park, there is a roller coaster that sends an average of three cars through its circuit every minute between 6pm and 7pm. A random variable, X, represents the number of roller coaster cars to pass through the circuit between 6pm and 6:10pm. What is the probability that 35 cars will pass through the circuit between 6pm and 6:10pm?
We can use this information to calculate the mean and standard deviation of the Poisson random variable, as shown below:
The mean of this variable is 30, while the standard deviation is 5.477.