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The mean and variance of a binomial distribution are 8 and 4 respectively. What is P ( X =1) equal to?

Options

  1. A1 2¹²
  2. B1 2^8
  3. C1 2^6
  4. D1 2^4

Correct answer

A. 1 2¹²

Step-by-step solution

aligned & n p=8, n p q=4 & q= 1 2 , so p= 1 2 & n p=8, n 1 2 =8 n=16 aligned aligned & p( X =1)= ¹⁶ C ₁ ( 1 2 )¹⁵ ( 1 2 )^1 & =16 ( 1 2 )¹⁶= 1 2¹² aligned

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