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The mean and variance of a binomial distribution are 4 and 3 respectively. Then the probability of getting exacatly six successes in this distribution

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The mean and variance of a binomial distribution are 4 and 3 respectively. Then the probability of getting exacatly six successes in this distribution, is A. .16C6( 1 4 )6( 3 4 )10 B. .16C6( 1 4 )16( 3 4 )20 C. .16C6( 1 4 )8( 3 4 )12 D. .16C9( 1 4 )16( 3 4 )20 Select the correct answer from above options

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Correct Answer - A Let X˜B(n,p) be a binomial variate with mean 4 and variance 3. Then, np=4,andnpq=3⇒q= 3 4 ,p= 1 4 andn=16 ∴P(X=r)=.16Cr( 1 4 )r( 3 4 )16-r,r=0,1,2,....,16 ⇒P(X=6)=.16C6( 1 4 )6((3)/(4))10

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