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S3 Mod 12 Nearly Normal – Act 2 – Exploration 2 Pg 349 names: First, complete the table by finding the relative frequency: Simulating May Precipitation Using 12 Coins Precipitation (cm) # of heads Frequency Relative Frequency [0, 2) [2, 4) [4, 6) [6, 8) [8, 10) [10, 12) [12, 14) [14, 16) [16, 18) [18, 20) [20, 22) [22, 24) [24, 26) 1) mean: 2) 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 2 7 11 25 23 13 12 4 2 1 0 Using the sample data provided find the following data in terms of number of heads: median: standard deviation: a) draw a relative frequency histogram and b) a relative frequency polygon for the number of heads. On the x-axis – of each of these: o identify and label where the mean occurs o identify and label the x-values 1 standard deviation on either side of the mean o identify and label the x-values 2 standard deviations on either side of the mean y x 3) Determine the theoretical probability distribution for 12 coins (Hint: Pg 346 Discussion 1 question a…Pascal’s triangle) o create a table showing # of heads, Frequency, Probability o create a relative frequency polygon of this distribution Number of Heads Frequency 0 1 2 3 4 5 6 7 8 9 10 11 12 1 12 Probability 924 66 y x 4) Use the formulas np and np(1 p) to calculate the mean and standard deviation of the binomial distribution for tossing a coin 12 times and counting the number of heads that appear. np : Compare these to your values from #1. np(1 p) :