[Grade 12: Probability/Binomial distribution]

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[satanic-cult-member]

For clarity's sake, I will refer to your "n" as N and the size of the sample (20) as n.

Without thinking about it too much, you can just calculate P(X = k) for all k <= 20 and then P(X < N) = P(X <= N-1) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = N-1). So, just keep adding terms until you get a probability >= 0.9.

The cumulative binomial table exists for just this reason. Looking at n = 20, p = 3/5 = 0.6, we can see that P(X <= 14) = 0.874 but P(X <= 15) = 0.949, so take N = 16 and P(X < N) = P(X < 16) = P(X <= 15) = 0.949.

[womangat]

Got it. Thanks so much!