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Manipal MET2016MathematicsProbability

If X follows a binomial distribution with parameters n=8 and p= 1 2 , then P(|x-4| 2) is equal to

Options

  1. A119 128
  2. B116 128
  3. C29 128
  4. DNone of these

Correct answer

A. 119 128

Step-by-step solution

We have, aligned & P(|x-4| 2)=P(-2 x-4 2)=P(2 x 6) & =1-[P(x=0)+P(x=1)+P(x=7)+P(x=8)] aligned =1- [ ^8 C₀ ( 1 2 )^8+ ^8 C₁ ( 1 2 )^8 . .+ ^8 C₇ ( 1 2 )^8+ ^8 C₈ ( 1 2 )^8 ]=1- ( 1 2 )^8(1+8+8+1)=1- 18 2^8 = 119 128

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