Question 797724
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The probability of *[tex \Large k] successes in *[tex \Large n] trials where *[tex \Large p] is the probability of success on any given trial is given by:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(n;k,p)\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k}]


Where *[tex \LARGE {{n}\choose{k}}] is the number of combinations of *[tex \Large n] things taken *[tex \Large k] at a time and is calculated by *[tex \Large \frac{n!}{k!(n\,-\,k)!}]


For your problem a):  *[tex \Large n\ =\ 60], *[tex \Large k\ =\ 35], and *[tex \Large p] you didn't bother to share.


For your problem b):  *[tex \Large n\ =\ 60], *[tex \Large k\ =\ 40],  *[tex \Large p] you didn't bother to share, and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(n;\geq k,p)\ =\ \sum_{i\,=\,k}^n\,{{n}\choose{i}}\left(p\right)^i\left(1\,-\,p\right)^{n\,-\,i}].


*[tex \Large i] ranges from 40 to 60, 21 terms total.


For problem c): *[tex \Large n\ =\ 60], *[tex \Large k\ =\ 20],  *[tex \Large p] you didn't bother to share, and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ P(n; < k,p)\ =\ \sum_{i\,=\,0}^{k-1}\,{{n}\choose{i}}\left(p\right)^i\left(1\,-\,p\right)^{n\,-\,i}]


*[tex \Large i] ranges from 0 to 19, 20 terms total.


If you are either lazy, very smart, or both, Excel has a built-in function called BINOMDIST that calculates this stuff as fast as you can hit the enter key.  Read the function help to learn how to use it.  BTW, if you are on a Mac, the Numbers application has the exact same function that works the exact same way, at least from the user's point of view.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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