Background:A renowned chocolatier claims their signature chocolate bars are always precisely 110 grams, with a variance of 32 grams squared due to the handcrafted nature of their products. You, a quality control analyst, are skeptical and decide to investigate if the chocolatier's claim holds.Objective:[br]Your mission is to analyze samples of chocolate bars to determine if they indeed average 110 grams with the variance stated.Investigation Steps:[list=1][*]Understanding the Distribution:[list][*]You'll assume the weight of chocolate bars follows a normal distribution.[/*][*]The theoretical distribution has a mean (μ) of 110 and a variance (σ^2) of 32.[/*][/list][/*][*]Sampling:[list][*]You decide to take random samples of size 6 from the production line.[/*][*]You will repeat this process 100 times to create a dataset of sample means.[/*][/list][/*][*]Statistical Analysis:[list][*]Analyze the sample means to determine if they align with the chocolatier's claim.[/*][*]Compare the experimental mean and variance to the theoretical values.[/*][/list][/*][*]Central Limit Theorem:[list][*]Explain how the Central Limit Theorem applies to the distribution of your sample means.[/*][*]How does the distribution of sample means compare to the original distribution of individual chocolate bar weights?[/*][/list][/*][*]Decision Making:[list][*]Based on the observed sample mean and variance, decide if the chocolatier's claim is likely to be true.[/*][*]What would be the implications if the actual average weight is significantly different from 110 grams?[/*][/list][/*][/list]Questions for Investigation:[list=1][*]Discovery Question:[list][*]If you found the average weight of your samples to be significantly more or less than 110 grams, what could be some potential reasons?[/*][/list][/*][*]Understanding Variance:[list][*]How would you explain the concept of variance to someone with no statistical background, using the chocolate bar weights as an example?[/*][/list][/*][*]Real-world Applications:[list][*]Why is it important for the chocolatier to maintain the weight close to 110 grams, and what could be the consequences of failing to do so?[/*][/list][/*][*]Reflection:[list][*]How does understanding sampling distribution help businesses ensure quality control?[/*][*]What are some limitations of using sample data to estimate population parameters?[/*][/list][/*][/list]