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When the event of interest is a cumulative event.

For example, to find the probability of getting three Heads in 8 tosses of a fair coin you would use the regular binomial distribution. But to find the probability of up to 3 Heads you would use the cumulative distribution.

This is because

Prob("up to 3") = Prob(0 or 1 or 2 or 3) = Prob(0) + Prob(1) + Prob(2) + Prob(3) since these are mutually exclusive.

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Q: When to use cumulative binomial probability?
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The probability that an individual is left handed is 0.1 In a class of 30 students what is the probability of finding at least 5 left hander's?

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