Scenario: At the start of many athletic competitions, team captains are asked to participate in a coin toss to determine how a competition starts. As an official of collegiate basketball games, Jeff has collected data on the coin tosses at the start of each game. He watches his officiating partner use the same coin at every competition and is now wondering if by chance the coin is weighted. Out of the 68 coin tosses Jeff has witnessed, heads came up 42 times. Your task is to determine if the coin is weighted or not but more importantly provide a convincing argument for your conclusion! Procedure : Simulation # of heads 39 1. Use the website to simulate the flip of 68 normal coin tosses and 2 29 record how many heads resulted in the chart at the right. We don't 33 need to know the number of tails. For example, in the 4 40 simulation done below, there were 38 heads out of 68 normal 5 30 coin tosses. 6 Show Cumulative Stats 7 Yes Number of Tosses: 68 Toss ' em! 8 21 No 9 30 10 34 11 3 4 Clear Results 12 39 13 34 Display Results: 14 32 Number List of 15 27 Choose Table Table Heads Tails Tosses 16 20 38 30 68 17 38 35 Shodor 18 19 40 20 32 2. Be sure to CLEAR RESULTS after each trial or choose "No" in 21 38 the Show Cumulative Stats box. Repeat the simulation 35 times 22 and record your data in the chart to the right. This collected data 23 30 MUST be in your assignment write up! 24 38 25 32 26 33 27 32 3. Once the chart is completed to the right, compute the total 28 30 number of times a normal coin was flipped. Hint-you flipped it 29 68 times for each row in the chart!! 30 32 31 34 68 ( 35 ) = 2380 32 40 33 32 34 3 60 35 38 4. Use your graphing calculator to compute the mean and explain how it relates to the scenario-the coin flipping. In other words, what does it tell us about a normal coin? 5. Use your graphing calculator, to compute the standard deviation and explain how it relates to the scenario. In other words, what does it tell us about a normal coin? 6. Sketch and label a normal distribution curve based on your calculated mean and standard deviation from #4 & #5. Be sure both axes are labeled appropriately for the problem! 6. Using the mean and standard deviation you computed above, calculate the z-score for the official Jeff has been witnessing who has flipped 42 heads in 68 coin tosses. 7. Do you feel that the official Jeff has been witnessing is using a weighted coin? Justify your response. I am looking for your understanding of mean, standard deviation, z- score and corresponding percentile in this analysis. Be sure to include an explanation of the meaning of all of these statistical values in your justification. Remember, you aren't writing this for your college instructor, but rather an audience of officials that would be incredibly interested in knowing if a coin used in coin tosses is weighted or not! And this could get an official fired
