AP EAMCET · Maths · Probability
If the mean and variance of a binomial variate \(X\) are 8 and 4 respectively, then \(P(X < 3)\) equals to
- A \(\frac{265}{2^{15}}\)
- B \(\frac{137}{2^{14}}\)
- C \(\frac{137}{2^{16}}\)
- D \(\frac{265}{2^{16}}\)
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 \(\quad n\left(\frac{1}{2}\right)=8 \Rightarrow n=16\)…
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