I am given a question saying "Let X be a binomial random variable with n = 150 and p = .382; find P(X = 32) and P(X <= 30)." In order to solve this, I feel like I have to use the binomial distribution: (nCx)(p^x)[(1-P)^(n-x)] but since n = 150, my calculator spits out "OVERFLOW". is there a way to solve this in such a way without using online calculators and excel formula functions? I'd like to get prepared if this kind of question comes up in an exam where I can only depend on my scientific calculators. Thanks.
2026-03-29 02:12:28.1774750348
finding the combination (nCr) when n is greater than 150!
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When $n$ is large, it is enough to use the normal distribution to approximate the binomial. Many standard scientific calculators choke on 69! or so.
To do this, the mean will be $np$, the number of trials times the probability of success, and the variance is $npq$, just the mean times the probability of failure.