2% of the total population arrested each year sounds like a lot! If we believe chatgpt, then the median time in prison is a couple of months. I'm unsure about

2% of the total population arrested each year sounds like a lot! If we believe chatgpt, then the median time in prison is a couple of months. I'm unsure about the math: "The arrival rate $\lambda$ is the rate at which people arrive in the queue, and the service rate $\mu$ is the rate at which people are served and leave the queue. In a stable system, the service rate must be greater than the arrival rate, otherwise the queue will grow indefinitely. Given that the total number of people in the queue $n$ is 1750000 and the arrival rate $\lambda$ is 600000 people per year, we can find the service rate $\mu$ by dividing the total number of people in the queue by the arrival rate: $\mu = \frac{n}{\lambda} = \frac{1750000}{600000} \approx 2.92$ people per year. This means that on average, about 2.92 people are served and leave the queue every year. The median waiting time in the queue can be calculated using the formula for the median of an exponential distribution, which is $\frac{\ln(2)}{\mu}$. So, the median waiting time in the queue in years is $\frac{\ln(2)}{2.92} \approx 0.237$ years."