Today's Notes

In today's note, we further our knowledge of Theoretical Binomial Distribution and learning how a mean is developed through Binomial Distribution. TBD is the method of estimating what the percentage of the outcomes would be before doing the experiment itself. On a graph, a TBD histogram would have a symmetrical look whilst the actual experiment has an assymmetrical look.

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The method for finding the TBD that uses specific details is the same method as we have done in our Probability unit. Yet there is an easier way using our graphing caluclators. Through the use of the Binomial Probability Distrobution Function we could quickly identify the success chances for each and every outcome. To use it, go into your distribution menu and select binompdf. From there, input number of trials first, then the probability of success. If you wish, you could input an optional command and input the specific outcome, if you're only interested in one outcome. Though binompdf would not be the used if the problem asks for something more (or less).

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In the case that it is not wise to use binompdf we would use binomcdf, or Binomial Cumulative Probability Distribution Function. To use it, binomcdf is right beneath binompdf. From there, it would be the same as we have done for binompdf. Except, that we add in the third value "- 1". We subtract 1 from the third option as it would add in an undesired value into the calculation. Binomcdf works similiarly like the invNorm function, so it would be wise to subtract from 1 sometimes.

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In addition to all of this, we have learned how the Binomial Distribution affects the mean. Each time the number of trials are increased (or decreased), the mean will always hop to different number, albeit it that looks the same. Though with each additional trials, a histogram would start to look like a Normal Curve. By increasing or decreasing the probability of success, the mean would also hop to a different number, moving the histogram horizontally on the scale.

Examples(s):

An example of this would be in this website:
http://www.math.uah.edu/stat/applets/binomialcoinexperiment.xhtml

Done for today, next scribe is Amanda or Eugene.