Statistical Analysis of Delivery Truck Weight Limit Risks

Quantitative and Analysis Project Tenisha Snipes American Intercontinental University Instructor: Christopher Guillory 10/11/2023

Statistical Analysis Abstract In today's technology-driven world, data is collected, analyzed, and interpreted to solve a wide range of business problems. Data analysis can be used in different methods, such as descriptive, diagnostic, predictive, or prescriptive, depending on the goal and the data. When we analyze and think about different topics, statistics plays a role in how we make sense of different data trends, how we research it and how we calculate it to use it for our own benefit. Mean, average, and standard deviation are statistical measures used to describe the distribution of a dataset. The standard deviation determines the spread of the distribution, that is, the amount of variation relative to the center. More importantly, it determines the average distance of the observations to the mean. In this research, we will be focused on determining the probability of our delivery truck making a successful and safe delivery. My breakdown will include all calculations and an explanation on how we calculate each area to come up with a resolution. What we know is we have a delivery truck, needing to deliver 71 boxes of A1 ball bearings. The delivery truck will be traveling over a bridge with a weight limit of 11,500 lbs. An empty delivery truck with a driver weighs 8500 lbs.

Statistical Analysis I will go through the process of the scenario on how I determined my answer based on factual details and thorough observations. Many of the details I’m going to share about this process is going to take a lot of researching, analyzing data, diagnosing and being able to predict outcomes. Researchers have proposed various statistical indices to assess the test security, and one most often used index is the average test-overlap rate, which was further generalized to the item pooling index (Chang & Zhang, 2002, 2003). When I conclude my research paper, we will have a better understanding of the standard deviation of mean, median and mode. I will also be able to determine if the truck will make it across the bridge safely based on the calculations or if the driver needs to turn around and end the delivery. The facts that we know are:  An empty delivery truck with the driver weighs about 8500 lbs.  We have 30 boxes of A1 ball bearings in the plant.  We immediately had them weighed.

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Statistical Analysis Introduction In this report I will be taking steps to determine the probability that a delivery truck weighing 11,500 will be able to cross a bridge with the weight limit being either over or under the weight limit. The assignment states to pretend you are a Business Analyst working for the ABC Ball Bearing company. I’m planning to send an order of 74 boxes of your A1 ball bearings to a customer on your delivery truck. I just found out that my truck will be going to go over a bridge that has a weight limit of 11,500 lbs. You need to determine if your truck will safely make it over the bridge. If you determine that the truck cannot make it over the bridge, you will need to call the driver and have him/her turn back. The process for determining the outcome will be in the steps taken below: • Work out the mean (the simple average of the numbers) • Subtract the mean from each number and square the result. • Find the mean of those squared differences. This is called the variance. • Take the square root of the variance. This is the standard deviation.

Statistical Analysis Scenario Analysis Calculate the Mean and the Standard Deviation of this sample. 40.1+41.1+39.5+40.1+39.1+41.2+37.6+39.1+41.6+40.8+43.2+38.9+38.1+43.5+36.9+39.1+40.5 +41.2+37.6+44.0+38.0+39.8+42.1+38.6+41.3+43.7+36.9+43.6+38.1+40.2 = 1,205.50/30 = 40.18333 Add all the decimal numbers in the data set chart then divide the total by the total numbers there are which are 30, which will give you 40.18333. The mean is rounded to one more decimal place than the original data which is 40.18. Standard Deviation Calculate the Maximum Average Weight of a Single Box- X=11,500-8,500=3,000 lbs

Statistical Analysis Using the normal distribution curve, calculate the probability that the truck’s total weight is under 11,500 lbs. What is your decision? Will you allow the truck to continue, or will you call the driver and tell him/her to turn back? Show all your calculations. To solve this problem, we must find the probability that the trucks limit is under 11,500 lbs. Weight limit 11,500. The total weight of the empty truck and driver is 8,500 pounds. The total weight of the 30 boxes of A1 ball bearings is 1,438.60 pounds. The total weight of the truck and the A1 ball bearings is pounds. 8,500 + 1,438.60 = 9,938.60 The total amount of pounds the truck will have been 9,938.60, so the truck can safely make it over the bridge since the weight of the truck is under the limit of 11,500. Calculate Z score. Bridge limit minus empty truck weight 11,500-8,500=3,000 X=11,500 u=3000/10=8.5 Z score is 8.5

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Statistical Analysis Discuss several types of sampling: i.e., convenience sampling, random sampling, stratified sampling, systematic sampling, or cluster sampling. Discuss which type of sampling is used in this scenario. 1. There are several types of sampling techniques. There is random sampling that involves randomly selecting data points from the dataset without any specific criteria. There is an equal chance that any given data point will be chosen. This technique is useful when the dataset is homogeneous, and each record is independent. 2. There is systematic sampling which involves selecting data points at regular intervals from an ordered dataset. For example, every nth data point is selected as part of the sample. Systematic sampling is easy to implement and can be more efficient than random sampling when the dataset is already sorted or ordered in some meaningful way. 3. A data sampling that divides the dataset into clusters or groups for analysis is cluster sampling. Instead of selecting individual data points, entire clusters are chosen randomly. Cluster sampling is useful when the dataset exhibits natural groupings or clusters, and it can be more efficient than random sampling if the clusters are internally homogeneous. 4. Stratified Sampling is dividing the dataset into distinct subgroups or strata based on specific characteristics or attributes. This sample is randomly selected from each stratum in proportion to its representation in the overall dataset. Stratified sampling ensures that each subgroup is represented in the sample, making it useful when the dataset has significant variations or imbalances.

Statistical Analysis 5. I feel that the sampling strategy that was used in this scenario based on all the details was the stratified random sampling because of the data displayed and different variations used to solve the outcome. Sampling Bias Based on the evidence, I do not feel that this scenario created a sampling bias because there could only be one theory in this situation. The truck could either cross the bridge due to being under the weight limit or it could not cross due to being over the weight limit. According to the Introductory Business Statistics textbook chapter 1.2 “states, when sampling bias happens, there can be incorrect conclusions drawn about the population that is being studied.” What does the central limit theorem state and why is it important to solving this problem. Are the thirty boxes of ball bearings enough to predict the probability of safely going over the bridge? The central limit theorem states that, if we have a population with mean and standard deviation and take sufficiently large random samples from the population with replacement, then the distribution of sample means will be approximately normally distributed.

Statistical Analysis Conclusion Statistics and probability are two fields that both use data to answer questions, but they do so in different ways. The field of probability uses existing known data to predict the likelihood of future events. The field of statistics uses data from a sample to draw inferences about a larger population.

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Statistical Analysis References 1.2 data, sampling, and variation in data and sampling - Introductory business statistics | OpenStax. (n.d.). OpenStax. https://openstax.org/books/introductory-business-statistics/pages/1- 2-data-sampling-and-variation-in-data-and-sampling Just a moment... (n.d.). Just a moment... https://www.wallstreetmojo.com/data-sampling Standard deviation formula and uses vs. variance. (2003, November 26). Investopedia. https://www.investopedia.com/terms/s/standarddeviation.asp Wang, C., Zheng, Y., & Chang, H. (2014). Does Standard Deviation Matter? Using "Standard Deviation" to Quantify Security of Multistage Testing. Psychometrika, 79(1), 154-174. https://doi.org/10.1007/s11336-013-9356-y

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