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 A:binompdf(, and then press ENTER.
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After trials: type 4 ENTER, after p: type .41 ENTER, and after x value: type 3 ENTER. Then press ENTER twice more. See the results below.
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To 4 decimal places, the P(X = 3) = 0.1627.
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.
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After trials: type 4 ENTER, after p: type .41 ENTER, and after x value: type 3 ENTER. Then press ENTER twice more. See the results below.
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To 4 decimal places, the
P (X
3) = 0.9717.
:
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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