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Question
Determine the binomial distribution where mean is 9 and standard deviation is `3/2` Also, find the probability of obtaining at most one success.
Solution
E(X) = 9 = nP .........(1)
`therefore 9/4 = npq `
`therefore 9/4 = 9 xx q`
`therefore q = 1/4 therefore p = 3/4`
`9 = 3/4n rArr n = 12`
`P(X = x)=^12C_x (3/4)^x(1/4)^(12-x)` ...........(0 ≤ X ≤ )
P(X ≤ 1) = P (X = 0) + P (X = 1)
`= ^""12C_0 (3/4)^circ (1/4)^12 + ^12 C_1 (3/4)^1 (1/4)^11`
`= (1/4)^12 + 12 xx 3/4 xx (1/4)^11`
`= (1/4)^12 (1+36)`
`= 37/4^12 = 37/2^24 = 0.0000022054
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