SOLUTION: If X has the binomial distribution with mean 25 and probability of success 1/5, find P(X<mean-[2*Sigma]) Thanks in advance.

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Question 1086415: If X has the binomial distribution with mean 25 and probability of success 1/5, find P(X Thanks in advance.

Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The mean of a binomial distribution is equal to n*P where n = the number of trials and P is the probability of success.
The number of trials is therefore equal to 25/(1/5) = 125
The standard deviation, sigma = sqrt(nP(1-P)) = sqrt((125/5)*(4/5)) = sqrt(20)
So we need to find the cumulative probability for X < 25 - 2*sqrt(20) = 16.06
Since we require a discrete number of trials, we take n = 16.
I get P = 0.0131 when I compute the cumulative probability.