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Let X be a binomially distributed random variable with mean 4 and variance 4 3 . Then 54 P X ≤ 2 is equal to

Options

  1. A73 27
  2. B146 27
  3. C146 81
  4. D126 81

Correct answer

B. 146 27

Step-by-step solution

Mean n p = 4 Variance n p q = 4 3 i.e. n = 6 ,   p = 2 3 ,   q = 1 3 Now 54 P X ≤ 2 = 54 P X = 2 + P X = 1 + P X = 0 = 54 C 2 6 2 3 2 1 3 4 + C 1 6 2 3 1 1 3 5 + C 0 6 2 3 0 1 3 6 = 54 15 × 4 3 6 + 6 × 2 3 6 + 1 3 6 = 2 × 3 3 73 3 6 = 146 27

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