Calculating a Binomial Probability

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Finding :

In mathematics, to calculate the binomial probability, P(X = x), we use the formula . The TI-83/84 has this formula already built in. The calculator function is binompdf (n, p, x).

To calculate P(X=3) given n = 4, p = 0.41, and q = 0.59, press 2nd VARS [DISTR], ARROW DOWN to select 0:binompdf(, and then press ENTER.

 
 
 

After binompdf( type 4,.41,3), and then press ENTER. See the results below.

 

To 4 decimal places, the P(X = 3) = 0.1627.


Finding :

To calculate the probablity P(X x) by hand, we would have to calculate each individual probability, P(0), P(1), P(2), ..., P(x), and then add those together. The TI-83/84 calculator has a built in function that does this calculation in one step. The function is binomcdf (n, p, x).

To calculate P(X 3) given n = 4, p = 0.41, and q = 0.59, press 2nd VARS [DISTR], ARROW DOWN to select A:binomcdf(, and then press ENTER.

 
 
 

After binomcdf(, type 4,.41,3), and then press ENTER. See the results below.

 

To 4 decimal places, the P (X 3) = 0.9717.


Finding :

To find use the fact that = 1 - P (X x - 1).

Thus to find P (X 3) given n = 4, p = 0.41, and q = 0.59, compute 1 - P(X 2) using binomcdf(4,.41,2) as is done directly above.



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