Binomial probabilities may be obtained using ...
Excel
In Excel, the function "BINOM.DIST()" can be used to find binomial probabilities. For example, if \(X \sim \BinomDistn(n=20, \pi=0.3)\),
Scientific calculator
If \(X \sim \BinomDistn(n=20, \pi=0.3)\) then a scientific calculator can find:
Probabilities for ranges of counts
Care must be taken with the wording of questions — should the 'extreme' value that is mentioned in the wording of the interval be included? For example,
In words... | In terms of X | Using ½ |
---|---|---|
More than 5 | X > 5 | X > 5.5 |
Greater than or equal to 5 | X ≥ 5 | X > 4.5 |
No more than 5 | X ≤ 5 | X < 5.5 |
At least 5 | X ≥ 5 | X > 4.5 |
Fewer than 5 | X < 5 | X < 4.5 |
5 or fewer | X ≤ 5 | X < 5.5 |
The final column most clearly expresses which values of \(X\) are included.
We recommend translating any interval into its form using ½ before finding its probability.
Translating the interval in this way is particularly useful when using a normal approximation to evaluate the probability. In this context, it is called a continuity correction.