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## Finding a Mall Parking Spot Using Mathematics – Part II

If you read the previous article on this topic, I imagine you were quite awakened by the nature of its content. How we use math to find a parking spot at a mall isn’t something you typically hear people talk about at their Christmas parties. However, I think anyone with a modicum of human interest would find this a very interesting topic of conversation. The reaction I usually get is one of “Wow. How do you do that?”, or “Can you really use math to find a parking space?”

As I mentioned in the first article, I was never content to get my math degrees and then do nothing with them other than take advantage of job opportunities. I wanted to know that this newfound power that I feverishly studied to obtain could actually be for my personal benefit: that I would be able to be an effective problem solver, and not just for those highly technical problems, but for more problems as well. everyday like now as the case in question. Consequently, I am constantly probing, thinking, and looking for ways to solve everyday problems, or to use math to help optimize or streamline an otherwise mundane task. This is exactly how I came up with the solution to the mall parking problem.

Basically, the solution to this question arises from two complementary mathematical disciplines: Probability and Statistics. These branches of mathematics are generally referred to as complementary because they are closely related and one must study and understand probability theory before one can strive to tackle statistical theory. These two disciplines help to solve this problem.

Now I’ll give you the method (with some reasoning, don’t be afraid, as I won’t go into laborious mathematical theory) on how to find a parking spot. Try it and I’m sure you’ll be amazed (just remember to drop me a line about how awesome it is). Ok, on to the method. Understand that we’re talking about finding a spot during peak hours when parking is hard to come by; obviously, no method would be needed under different circumstances. This is especially true during the Christmas season (which is actually the time of writing this article, as it happens).

Ready to try this? Here we go. The next time you go to the mall, choose a waiting area where you can see a total of at least twenty cars in front of you on either side. The reason for number twenty will be explained later. Now take three hours (180 minutes) and divide that by the number of cars, which in this example is 180/20 or 9 minutes. Look at the clock and note the time. Within nine minutes from the time you look at the clock, often quite a bit sooner, one of these twenty places will open. The math pretty much guarantees it. Whenever I try it and especially when I demonstrate it to someone, I am always amused by the success of the method. While others are feverishly circling the lot, you sit there patiently watching. Choose your territory and just wait, knowing that in a few minutes the prize is won. How smug!

So what guarantees that you will get one of these places in the allotted time. This is where we start using some statistical theory. There is a well-known theory in Statistics called the Central Limit Theory. What this theory essentially says is that, in the long run, many things in life can be predicted by a normal curve. This, you may recall, is the bell-shaped curve, with the two tails extending in either direction. This is the most famous statistical curve. For those of you wondering, a statistical curve is a graph from which we can read information. This graph allows us to make educated guesses or predictions about populations, in this case the population of cars parked at the local mall.

Graphs like the normal curve tell us where we are in height, let’s say, with respect to the rest of the country. If we are in the 90th percentile for height, we know that we are taller than 90% of the population. The central limit theorem tells us that eventually all heights, all weights, all IQs in a population smooth out to follow a normal curve pattern. Now what does “eventually” mean? This means that we need a certain population size of things for this theorem to apply. The number that works very well is twenty-five, but for our case, twenty will generally be sufficient. If you can have twenty-five or more cars in front of you, the method works best.

Once we’ve made some basic assumptions about parked cars, statistics can be applied and we can start making predictions about when parking spaces will be available. We can’t predict which of the twenty cars will come out first, but we can predict that one of them will come out in a certain time period. This process is similar to what a life insurance company does when it is able to predict how many people of a certain age will die in the next year, but not which ones will die. To make these predictions, the company relies on so-called mortality tables, and these are based on probability theory and statistics. In our particular problem, suppose that in three hours all twenty cars will have been turned around and replaced by another twenty cars. To reach this conclusion, we used some basic assumptions about two parameters of the Normal Distribution, the mean and the standard deviation. For the purposes of this article I will not go into the details about these parameters; the main purpose is to show that this method will work very well and can be tried next time.

In short, pick your spot in front of at least twenty cars. Divide 180 minutes by the number of cars, in this case 20, to get 9 minutes (Note: for twenty-five cars, the time interval will be 7.2 minutes or 7 minutes and 12 seconds, if you really want to be precise). ). Once you’ve set your time slot, you can check your watch and make sure a spot will be available within 9 minutes, or whatever interval you’ve calculated based on the number of cars you’re working with; and that due to the nature of the Normal curve, a place will often become available before the maximum allotted time. Try this and you will be surprised. At the very least, you’ll earn points with friends and family for your intuitive nature.

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