The mean and varaince of binomial distribution are 4 and 3, respectively. Then, the probability of getting exactly six success in this distribution is

Options

A. `.^(16)C_(6)(1/4)^(6)(3/4)^(10)`
B. `.^(16)C_(6)(1/4)^(6)(3/4)^(20)`
C. `.^(16)C_(6)(1/4)^(8)(3/4)^(12)`
D. `.^(16)C_(9)(1/4)^(16)(3/4)^(20)`

Answer

A

Explanation

Given `np=4,npq=3`
`impliesp=1/4,q=3/4`
`nxx1/4=4`
`impliesn=16`
`:.p(X=6)=.^(16)C_(6)(1/4)^(6).(3/4)^(10)`