Use the formula provided in question C to calculate the expected standard deviation for experiments with F = 100 or F = 1000 coin flips. How does the expected standard deviation for the number of heads in experiments with 100 coin flips compare to the standard deviation that you calculated for the column of 10 totals? Since we only have one joint sample of 1000 flips, we cannot estimate the standard deviation experimentally (feel free to take several samples of 1000 flips if you have the energy!). However, we can ask if the grand total was within about 1 standard deviation of the expected mean (500 heads out of 1000). By how many expected standard deviations did your grand total differ from the expected mean? Comment on your results. C. As hinted in the introduction, there is a very important rule of thumb for statistical processes that you should learn: the size of the fluctuations is proportional to the SQUARE ROOT of the number of data points. In this case, it turns out that the theoretical "true" standard deviation for coin flips is half of the square root of the number of flips F, like so: o = √F/2. This can be proved mathematically, based on the "number of ways" to achieve each outcome... things that can be achieved in more ways are more likely! For F = 10 flips, we have an expected standard deviation of √10/2= 1.58. So, 5 ± 1.6 heads is a very typical expectation for 10 flips. But, recall that statistical fluctuations of more than 2 standard deviations, i.e. more severe than 5 ± 3.2 heads here, happen about 5% of the time, so even that is not so rare! How did your ten estimators of the standard deviation for 10 flips compare to the expected value of 1.58? Comment on your interpretation (next page).