Project #2: Binomial Experiment using StatDisk Math 150 Due: Nov 8, 2017

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1 Project #2: Binomial Experiment using StatDisk Math 150 Due: Nov 8, 2017 Purpose of Project: 1) Gain a better understanding of binomial distributions; 2) Use statdisk to create binomial distribution charts; 3) Read and interpret data from binomial experiments Instructions: You may work in pairs on this project. If you work in pairs turn in ONE project only. The purpose of these projects to help you better understand the material we are covering. Use it for that purpose and do your OWN work. I take plagiarism seriously, so your work or your group s work should be your own. Any duplicate work received will earn a ZERO for all parties involved, along with a referral for academic dishonesty. This may be turned in via (using a well-labeled file name) or on paper. Either way, you need to submit the grading rubric with your name(s) and file number(s) to me in class. Description of Binomial Experiment: A binomial experiment is an experiment where you have a fixed number of independent trials with only two outcomes. For example, the outcome might involve a yes or no answer. If you toss a coin you might ask yourself Will I get a heads? and the answer is either yes or no. That s the basic idea, but in order to call an experiment a binomial experiment you also have to make sure of the following three rules: Rules for Binomial Experiment 1. You must have a fixed number of trials. This should go without saying; if you don t have a fixed number of trials you could be tossing that coin forever without stopping. In addition, the results from your experiment will be vastly different if you toss that coin twice (you could get two heads in a row and conclude that you will always get a heads if you toss a coin!) or if you toss it a hundred times. 2. Each trial is independent of the others. Independent means that every time you repeat the trial (i.e. tossing that coin), it s a fresh new trial and nothing you do has an effect on each coin toss. For example, if you tossed ten coins at a time and removed the coins that landed heads down before throwing again, you ll affect the probability, because there are fewer coins. There s nothing wrong with that, but it would not be a binomial experiment! The fact that each trial is independent of each other leads to another important aspect of binomial experiments; the probability remains constant from trial to trial. 3. There are only two outcomes. In other words, if you can phrase the experiment as a yes or no answer, then it can be a binomial experiment: will I get a heads? Can someone find a parking space in the city? Do eggs hard boil in ten minutes? Examples of experiments that ARE Binomial Experiments Tossing a coin a hundred times to see how many land on heads.

2 Asking 100 people if they have ever been to Paris. Rolling two dice to see if you get a double. Examples of experiments that are not Binomial Experiments Tossing a coin until you get a heads (it could take one toss, or three, or six, so there is not a fixed number of trials) Asking 100 people how much they weigh (you ll have a hundred possible answers, not two) Part I You will now use Statdisk to create the chart to represent the following situation: Mrs. Martinez went to the local Piggly-Wiggly grocery store while visiting Chicago. She counted the number of laundry detergents on the shelf that were made by Proctor and Gamble: 7 out of 16 detergents. Open up a word document. Put your name and file number on the document. Title the document: Statdisk Project: Binomial Distributions Leave a few lines empty and then insert a 4 x 6 table into the document, like the one below. Label the columns as shown: x P(x) P(x or fewer) P(x or greater) Save your Word document Steps: 1) Open up Statdisk. 2) Click on Analysis, then Probability Distributions, then Binomial Distribution 3) Enter in Num Trials, n: 4 - the number of trials in the given situation 4) Enter in Success Prob, p: the probability of picking Procter and Gamble at my grocery store. (4/7 = ) 5) Click on Copy 6) Go to your table and highlight all the empty boxes (Do NOT highlight the top row with your titles.) Paste your data into the table. You should now have an exact replicate of what Statdisk gave you.

3 7) Note that Statdisk also gives you the Mean, Standard Deviation and Variance. Below the table, type in those values. Be sure to label them. 8) Now check to see if the formulas for calculating mean and standard deviation in a binomial distribution give you the same values given by Statdisk. Show the values that you entered in your calculator and the solutions. μ = n p σ = n p q (So far I have walked you through EVERY step. For the above formulas, I did not give you the value of q. You will need to use your knowledge of binomial distributions and your vocabulary from that section to get q. It is not a difficult value to calculate, but does require you to study your vocabulary.) Save your word document. Answer the following questions in complete sentences on your word document. Use the chart you created to help you get these answers. Do NOT just write a list of numeric answers. If you were to go to the Piggly-Wiggly that Mrs. Martinez went and picked 4 detergents randomly from the shelf. A) What is the probability that all of the products were Procter and Gamble products? B) What is the probability that exactly 3 products were Procter and Gamble products? C) What is the probability that at least 1 product was Procter and Gamble products? D) What is the probability that at most 1 product was Procter and Gamble products? E) What is the probability that none of the products were Procter and Gamble products F) What is the average number of Procter and Gamble products that would be picked? G) Using the range rule of thumb for usual values, what are the lowest and highest number of Procter and Gamble products you would expect to pick?

4 Part II This part requires you to go to a local store. Pick a grocery or drug store that offers multiple brand choices for the item you chose. (Stores like Costco would not work for this project as they only offer one or two options of a product. ) Do ONLY one of the Options below (not both). Be sure you have enough data to be able to do the at home portion of the project. (Hint: Read the entire project before going to the store, so you don t have to return to the store for data you didn t write down ) Option I: Get a notepad and go to your nearest store that sells laundry detergent. You will need to read labels, write down detergent brands and the manufacturers. You need to check EACH product to be sure you see how many are made by each manufacturer. You might be surprised by what you discover. Next, you need to pick a manufacturing company as your choice for success. You may choose Procter and Gamble or another company. It is more interesting if you pick a company that has at least 3 products on the shelf. Now use the information that you gathered to count the number of versions of laundry detergent that are made by the company of your choice. Then count the total number of detergent options in the store. Option II: Get a notepad and go to your nearest store and pick a product that has a lot of options that you are interested in investigating. This could be deodorant, toilet paper, soda, sports drink, peanut butter anything that has at least 10 different options of the same item. For example, soda could work if you limit yourself to just lemon-lime soda OR just cola. Bad choices would be jam or yogurt (lots of different flavors but not actually lots of different brand options). Be sure that you can answer the below questions for the product of your choice. Start by writing the product you chose. Then find the item in the store and begin by writing down the names and manufacturer for each. You will need to check the labels to get this info. You need to check EACH product to be sure you see how many are made by each manufacturer. You might be surprised by what you discover. Next, you need to pick a manufacturing company from your product choice, as your success. It is best if you pick a company that has at least 3 products on the shelf, or your numbers will be hard to work with. Now use your information to count the number of versions of your product that are made by the company of your choice. Then count the total number of options of that product in the store. Be sure to check with the instructor about your choice of data. I can help you make sure you are creating a binomial distribution and choose reasonable options (so you aren t counting 100 s of items). Your data values gathered should be different from everyone else in the class except your partner, so you also need to clear it with me so we don t have duplicate data.

5 At home: Open up your word document. Start a new page. Put a title on this page that refers to your product choice. What you will need to do: 1) Write a paragraph explaining what products you gathered your data from and what your statistics will be about. Also include in here the data that you collected. (If you fail to write this paragraph I will be unable to grade any work following it because this provides all the necessary information to do the rest of the work.) 2) You are going to create a binomial distribution for n = 5. Calculate the probability of picking a product made by your chosen company in the store you chose p = Explain how you know this values is correct. This should come from your data collection at the store. 3) Open Statdisk and create a binomial distribution using the above values. 4) Copy and paste the information into a chart on your word document. Be sure to include the column titles as you did in part I. 5) Copy (by typing) the μ, σ, σ 2 below your chart on the word document. Now answer the following questions with regard to your company choice. Again you must use complete sentences. This is a report about your product. You are going to use your binomial distribution and mean and standard deviaton from above to answer questions with regard to the following: If you were to send a friend to the store your chose to randomly pick FIVE different types of your product, what the probabilities of picking a product from your manufacturer. If your friend returns with the 5 items,. a) What is the probability that none of the products is from your company? b) What is the probability that at least one product is from your company? c) What is the probability that no more than three products are from your company? d) What is the probability that at most 4 product are from your company? e) What is the probability that all of the products are from your company? f) What is the average number of products from your company that would be picked?

6 g) Using the range rule of thumb for usual values, what are the lowest and highest number of your product you would expect to pick? Final Questions: (For students working in pairs. EACH of you should answer EACH of the four questions h, I, j & k, separately. Put your name next to your answers so I know whom to give credit for which answers. I.e. there should be two answers for each of the questions below. You may draw similar conclusions but your write-up should demonstrate your own personal understanding of the topic. Part k should demonstrate what you personally did on the project and what you personally learned.) h) What did you learn about the number of products that each company produces? i) Looking at the answers to the A-G and a-g, why do you think companies do this? I.e. what might help them make more money? j) It is important to note that besides quantity of products, companies also pay for location on shelves. Shelves at eye level are the most expensive to have your product placed. So, although this simple binomial distribution representation gives you a good idea of the probability of randomly picking a product there are also a lot more variables than just quantity. What other variables do you think affect people s choice of a product in the store? List at least three. Take your time to think about these and explain why you chose each. k) Your personal final comments. What did you learn from this project? Ideas of discussion items: Problems you had while trying to do the work and how you fixed them. What you learned about companies and their products. How companies likely use statistics in product creation, placement, etc. I m particularly interested in hearing your a-ha or Oh-my moment you had while trying to complete this project. Before turning this in: Create a title page with the name and file number of both people who worked on the project Check your work to be sure all the parts are labeled with the number or letter of the question you were answering. Write your names and file numbers on the rubric and attach it to the back of the project. Use a stapler or paperclip to keep project papers together. Do NOT use a folder, or plastic cover. Be sure to attach the grading rubric to the front or back of your project.

7 Project #2 - Binomial Distributions using StatDisk - Grading Rubric Part I: 1-5) binomial chart check μ, σ using formula A E) F) Average G) Range rule of thumb Part II: 1-5) Appropriate title and explanations n, p, μ, σ, σ 2 binomial chart a e) f) Average g) Range rule of thumb File # Name / 20 points / 35 points Final Questions: h) What you learned about the number of products produced per company. i) Why do companies produce so many products? Refer to A-G & a-g / 15 points j) What affects people s choice of product? k) Final comments Total = / 70 points Project #2 - Binomial Distributions using StatDisk - Grading Rubric Part I: 1-5) binomial chart check μ, σ using formula A E) F) Average G) Range rule of thumb Part II: 1-5) Appropriate title and explanations n, p, μ, σ, σ 2 binomial chart a e) f) Average g) Range rule of thumb File # Name / 20 points / 35 points Final Questions: h) What you learned about the number of products produced per company. i) Why do companies produce so many products? Refer to A-G & a-g / 15 points j) What affects people s choice of product? k) Final comments Total = / 70 points