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Transcript of Simulated Coins
The mean for the distribution of 25 simulated flips is .485 and the mean for the distribution of 100 simulated flips is .52. The distribution of proportions for each histogram are somewhat symmetrical and uni modal. When looking at the two you can see that for the 25 simulated flips distribution is spread out while the 100 simulated flips distribution is clustered around the mean.
What should have happened?
If we look at the normal model we see that 68% of the coin flips should have been between 45% and 55%, 95% of the coin flips should have been between 40% and 60%, and 99.7% of the coin flips should have been between 35% and 65%
Compare the actual distribution of your twenty sample proportions for 100 tosses to what the sampling model predicts.
When comparing the sample model to the distribution for 100 simulated coin flips you can see they both have one mode, both look loosely like a normal model, and both have a mean of around 50%, but the 100 coin flip simulation is skewed to the left.
Describe how your results might differ if you had run 100 trials of the simulation instead of only 20?
If we ran 100 trials instead of 20 we would expect the model of the sample to look much more like the normal model since the more trials we add the more our distribution will look like a normal model because of the central limit theorem.
By Jonathan Cajuste