Math& 146 Project3 Central Limit Theorem In this project, you will be exploring the Central Limit Theorem using a very simple game that uses a die. You will either need a physical 6-sided die or you can use a website such as: https://www.calculator.net/dice-roller.htm| (Dice Rgllgr igglgulamrng} Part 1 Generating Data Instructions: 1. Roll 3 die (physically or virtually) a. If you roll a 1, score 1 point in. If you roll a 5, score 5 points c. If you roll any other number, score 0 points 2. Roll a total of 30 times, recording your results in a table like the one below. Remember that your score for each roll should only ever be 0, 1, or 5. Example Table of Score results: Part 1 Questions: Use your results to do the following: 1) Make a histogram for the Part 1 results using at least 6 bars 2) Calculate the median score you rolled 3] Calculate the mean score 4] Calculate the standard deviation 5] Is the distribution symmetric or skewed? If skewed, then which way? Part 2 Generating Data Instructions: 1. Enter the mean of your previous 30 die rolls (your answer to question 3) into the table below. 2. Repeat the 30 die rolls {physically or virtually} and calculate the mean score twice more. Both times, enter your results (the mean score} in the table. 3. I have also done this 27 times and included my results in the table for you to use. (I'm sure you've had enough die rolling by nowl} Table of Mean Scores results: m \"Elm-W m Part 2 Questions: Use your results to do the following: 5) 7) 8) 9) Make a histogram for the Part 2 results using at least 6 bars (including your three calculated means and the 27 means I provided} Calculate the median of these (that is, the median ofthe mean scores} Calculate the mean of the mean scores Calculate the standard deviation of the mean scores 10) What is the shape of this distribution? Things to notice: We started with a very asymmetric distribution, as you say In Part 1. But, by taking the means of a lot of samples, we were able to create a distribution of sample means. This distribution, called the sampling mm is approximately normal, even for a relatively small sample size (only 30}. And this isn't a fluke; for any distribution that we might start with, the sampling distribution will be approximately normal if we take a large enough sample. This concept is called the W. That is, no matter what distribution you start with, the distribution of possible sample means will always be approximately normal for large enough samples. Part 3 Questions: Refer to your previous answers to answer the following questions in one or two sentences: ill How does the mean score from your first 30 rolls (question 3} compare to the mean score of the sampling distribution (question 8)? 12) How does the standard deviation from your first 30 rolls (question 4) compare to the standard deviation of the sampling distribution (question 9}? Additional Instructions: The project is submitted on Canvas and due by the end of the day listed. Your project should be typed or neatly hand-written and scanned. (You may nd Microsoft Lens or similar apps helpful for scanning a paper you've hand-written.) o The file should have an extension of .pdf, door, or .xlsx You are free to use technology on any part, including for graphing and computations. Neatness is important and will be considered in the grade. The grading rubric can be found in Canvas