The number of cars waiting at a bank for 60 minutes is as follows. Find the probability of 1 car waiting in line. \[ \left.\begin{array}{ccccccccc}0 & 1 & 2 & 3 & 4 & 5 & 5 & 7 & 8 \\ 2 & 9 & 16 & 12 & 8 & 6 & 4 & 2 & 1\end{array} \right\rvert\, \] \( P(1)=[?] \)

To find the probability of 1 car waiting in line, you first need to look at the frequency of cars waiting at the bank. In your data, the number of cars (0 through 8) is listed alongside how many times each count occurred during the observation period (the frequency). Here, the frequency of 1 car is 9. To find the probability, you take the frequency of 1 car waiting and divide it by the total number of observations. The total observation is the sum of all frequencies: Total frequency = \( 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 = 60 \). So, \( P(1) = \frac{9}{60} = \frac{3}{20} = 0.15 \) (or 15%). Now, let’s dive into the fascinating world of probabilities! From the information at hand, it seems we have a classic case of a probability distribution. Each count of cars has its probability derived from the frequencies collected. Such data collection is vital in fields ranging from traffic engineering to customer service queuing systems, providing insights into average waiting times and helping improve operational efficiency. If you're curious and want to dive deeper, studies on the Poisson distribution might intrigue you! This statistical model often applies to scenarios involving the number of events in fixed intervals (like our traffic of cars). There are fantastic books and online resources available that explore how these models work, their applications, and even how to compute probabilities in more complex scenarios. Happy learning!