BS2001_O_Ramirez

BS2001 Assessment Template Prepared by: Ophelia Ramirez Date: 10/14/2023 Walden University, CBE Business Statistics, Probability Theory, Use probability theory to predict outcomes

Probabilities and Probability Theory How Statistics Can Be Used Statistics is something that is very beneficial in running day-to-day operations in a business. One way statistics can be used is by measuring sales within a business. A business can keep track of what products are the most popular in sales and what products are the least purchased. When a business has this information available, they are able to determine what their customers like and they can come up with a plan on what they need to improve their sales. Statistics are part of our daily lives and sometimes, we do not even realize it. One way statistics can be used in our community is by the streets and maintenance department for your local city/county. One recent example I came across was a neighborhood community that wanted traffic lights installed at a specific intersection. Their claim was that the intersection having no traffic lights was the main cause of many deadly accidents that occurred there. Upon reviewing past data and running their statistics, they determined that installing traffic lights would become more beneficial to the community as a whole to minimize the car accidents. Unsurprisingly, this did help minimize the number of accidents drastically. Statistical Questions  How much does milk cost on the East coast of the United States? This is a statistical question because you would be comparing the prices of milk amongst different stores on the East coast of the United States.  How many minutes does it take to drive 30 miles at an average speed of 55 miles per hour? This is not a statistical question because you are not comparing the speed or distance to anything, you are only using a formula to calculate the time it would take to drive a certain distance at a certain speed.  What is the age difference between you and your siblings? This is not a statistical question because there are not many possibilities of answers you can compare since you are only calculating the age difference.  How many hours of sleep do teenagers get during the school year compared to summer vacation? This is a statistical question because this is a comparison you can make amongst a variety of teenagers to determine the average of when they sleep the most. Permutations and Combinations “A permutation or combination is a set of ordered things” (Glen, n.d.). There is, however, one major difference with these two terms. A permutation is when you put things together in order and a combination is when you put things together but not in order. When it comes to determining the number of ways an event can occur, it is best to use permutations rather than combinations because that is what will give you the most possibilities. Upon deciding to use the permutation formula, you can either use the formula if allowing repetitions or you can use the formula for no repetitions. The calculation for the Number of Combinations has one extra factor rather than the calculation for the Number of Permutations so the result for Combinations will always be smaller. When using the formula for the Number of Combinations, you are given an extra factor which is dividing the n! by r! (n-r)! . r! is the extra factor which results in having less possibilities. The formula for Permutations does not have that extra factor and only divides n! by (n-r)! which results in having more possibilities. Page 2 of 6

received in that year and then took the complaints in the Southeast region and divided them by the total number of complaints in 2017.  The probability that a complaint was from the Central region in 2018 is .339. To get this result, I only looked at the 2018 totals. Then I took the number of complaints received in the central region in 2018 and divided it by all of the number of complaints received in 2018.  The probability that a complaint did not occur in 2018 and was not from the Southeast region .250.  The probability that two complaints chosen at random are from the northeast region is .304. Probabilities There could be a total of 720 different teams that could be formed from the available individuals. The available individuals consist of 6 accountants, 5 production specialists, 3 finance specialists, and 8 management specialists. A team can only consist of 4 people which would consist of one of each type of specialists. What I had to do was multiple the following: 6 x 5 x 3 x 8 and it gave me the result of 720. Probabilities and Decision Making 1 st Probability 2 nd Probability 3 rd Probability 4 th Probability Total Probability (multiply all) Bert .7 .6 .5 .4 .084 Riley .56 .51 .46 .41 .054 I composed this table using the data provided in regards to the probability of closing after a certain percentage of probability drops by the following call. By creating this table, it gives me a visual of how much the probability drops after each call. With this in mind, by their fourth call, Bert’s probability of a sale will drop to 40% and Riley’s probability of a sale will be 41%. With Bert having a higher probability of closing on the first call, Bert has a higher probability of making a sale within 4 calls with is 8.4% compared to Riley which is 5.4%. Management should keep Bert and let Riley go. Probabilities and Decision Making 1st Decision 2nd Decision 3rd Decision 4th Decision 5th Decision P 0.8 0.8 0.8 0.8 0.8 0.32768 0.2 0.8 0.8 0.8 0.8 0.08192 0.8 0.2 0.8 0.8 0.8 0.08192 0.8 0.8 0.2 0.8 0.8 0.08192 0.8 0.8 0.8 0.2 0.8 0.08192 0.8 0.8 0.8 0.8 0.2 0.08192 In this case, Dave’s prospective employer has warned him he can only make one mistake and that he would get fired if he makes a second mistake. In order to find the total probability of Dave not being fired, I had to add every number in the last column (0.32768 + 0.08192 + 0.08192 + 0.08192 + 0.08192 + 0.08192). The solution to this is .73728 which is 73.7% probability of Dave not getting fired. In order for me to find the probability of Dave getting fired, I subtracted 73.7 from 100 and got 26.3. With this in Page 4 of 6

mind, Dave should decline the job opportunity and not take the risk since he has a 26.3% probability of getting fired. Probabilities and Predictions The information that is provided in this narrative is very helpful because it already gives us the average which is μ = .517 and it also gives us the standard deviation which is σ = .037. A new car model requires alloy sheets to be: P(0.495 < X < 0.525). After finding the z-scores, I determined that 31% of the sheets that are made by the mill will be suitable for the new car model. References Anywhere Math. (2016, February 22). Introduction to statistics [Video]. YouTube. https://www.youtube.com/watch?v=LMSyiAJm99g Glen, S. (2021, May 1). Arithmetic mean: Definition how to find it [Multimedia]. Statistics How To. https://www.statisticshowto.com/arithmetic-mean/ Glen, S. (n.d.). Mean, median, mode: What they are, how to find them [Multimedia]. Statistics How To. https://www.statisticshowto.com/probability-and-statistics/statistics- definitions/mean-median-mode/ Glen, S. (n.d.). Sample variance: Simple definition, how to find it in easy steps [Multimedia]. Statistics How To. https://www.statisticshowto.com/probability-and-statistics/descriptive- statistics/sample-variance/ Page 5 of 6