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TS EAMCET · Maths · Probability

If the mean and variance of a binomial variate \(X\) are 8 and 4 respectively, then \(P(X < 3)\) equals to

  1. A \(\frac{265}{2^{15}}\)
  2. B \(\frac{137}{2^{14}}\)
  3. C \(\frac{137}{2^{16}}\)
  4. D \(\frac{265}{2^{16}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{137}{2^{16}}\)

Step-by-step Solution

Detailed explanation

Given, mean of binomial variable, \(n p=8\) and variance of binomial variable, \(n p q=4\) \(\therefore \quad q=\frac{1}{2}\) and \[ \begin{aligned} p & =1-q \\ & =1-\frac{1}{2}=\frac{1}{2} \end{aligned} \] and \(\quad n\left(\frac{1}{2}\right)=8 \Rightarrow n=16\)…