Introduction to statistics
answer the following discussion questions:
1. What is the difference between saying that you should get “heads” about half the time when flipping a “fair” coin and the actual probability of getting 10 heads in 20 flips?
2. What applications does the probability distribution of shoppers have?
3. What other probabilities would you investigate and why?
Reopened:
1.
Below is the formula for excel that I used after looking at the handout:
=((FACT(20)/(FACT(20-10)*FACT(10)))*(0.5^10)*(0.5^10))
The formula yields 17.3% chance of success. I suppose I could be a little more enlightened. If you plug in 20 and 40 in place of 10 and 20 I get a lower percentage. I would think that the more you flip the closer to the “perfect scenario” you will get. We don’t live in a perfect world though, and I think it is important to remember that the 50% for heads or tails is only accounted for each flip, not a set of flips. That is the difference.
2.
Probability distribution on shoppers can give you statistics to create a more targeted shopping environment. For example you can take the probability of the age of shoppers. You could create a range for the age of maybe every 10 years starting with 18. You could find the distributions and use these to tailor the store to the greatest probability. Say that the results come out to a majority of elderly shoppers your store would need to have ease of access, scooter carts, or even automatic doors.
3.
It would be worth while to investigate which products are being bought. If a product has a distribution near 0, then it might not be worth to continue to sell that product. I suppose that’s relative and there are other variables. There are so many products that they all may be near 0 or something like 0.0000001. I suppose a more effective route would be to check which products have the highest and lowest markups. You would want your highest markup products to have the higher distributions while the lower markups to have the least because they won’t make you money. You could use these probabilities to shift around what you sell or provide ro maximize profits.
1) What is the difference between saying that you should get “heads” about half the time when flipping a “fair” coin and the actual probability of getting 10 heads in 20 flips?
About 83%. Meaning the idea sounds good that with a 50/50 chance in one flip of getting heads but in reality 10 heads in 20 flips presents a much different probability. I found the text a bit lacking and had to do some thinking. (I did this prior to the handout from Kris) These are independent outcomes for each flip so 2*2*2… (2^20) gives a staggering possible outcome of 1,048,576. To figure out the probability of heads occurring 10 times in 20 flips is not half of 1,048,576 but found with use of the combinations rule. Using the rule gives us 184,756 combinations of heads occurring 10 times so it’s a simple matter of calculating the probability from there. 184,756/1,048,576 ≅ .176 or about a 17.6% chance of exactly 10 heads in 20flips. So when asked what is the difference between the the expectation of half the time getting heads and reality I say about 83% so odds are it isn’t going to happen often.
2) What applications does the probability distribution of shoppers have?
This question threw me a bit and the Kris clarified to me: “I think you should approach the second question as one who is determining from perhaps a business owner’s perspective how to evaluate the busiest times of shopping.”
With that said, evaluating the busiest times of shopping can vary by the store, operating hours and location. Narrowing the field to say a grocery store, I would break up the hours open into segments either 1 or 2 hour windows. I’m sure any current POS system timestamps the transactions so at the end of a day tallies can be made of all transactions and their respective windows. This process I would note for at least a full week and the more data the better so probably two weeks to a month. With this information I would be able to graph expected transactions on any given day and time window and see what is the busiest time. With that information I would make sure I had enough staff to cover all aspects of stocking/checkout etc. while in slower periods I could reduce the worker count and save some money. This information is also good for in-store promotions to maximize the shoppers available to reach.
3) What other probabilities would you investigate and why?
I would expand the data from the above to sample different seasons of the year i.e. daylight savings time or summer vs winter. Is my store in a weather adverse location where snow and rain is a problem or is it sunny most of the year? The odds of inclement weather affect deliveries, operations and sales volume. If I dealt with multiple stores performance between stores could also be measured. I suppose there is a whole science to moving product off shelves with marketing, but maybe tracking as well what department moves the most during those peak periods and see if there are any corollaries to find that can help with profitability. Demographics is a big data set as well. Do the products stocked cater to the needs of the locals? These were pretty general questions but these were some of the specifics I thought of.
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