# Determine the Binomial Distribution Where Mean is 9 and Standard Deviation is 3 2 Also, Find the Probability of Obtaining at - Mathematics

Sum

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

Concept: Bernoulli Trials and Binomial Distribution
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