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TS EAMCET · Maths · Statistics

Let \(X \sim B(n, p)\) with mean \(\mu\) and variance \(\sigma^2\). If \(\mu=2 \sigma^2\) and \(\mu+\sigma^2=3\), then \(P(X \leq 3)=\)

  1. A \(\frac{15}{16}\)
  2. B \(\frac{2}{3}\)
  3. C \(\frac{14}{17}\)
  4. D \(\frac{1}{3}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{15}{16}\)

Step-by-step Solution

Detailed explanation

As we know that, mean \(=\mu=n p\) and variance \(=\sigma^2=n p q\) Since it is given that, \(\mu=2 \sigma^2\) \(\Rightarrow \quad n p=2 n p q \Rightarrow q=\frac{1}{2} \quad \therefore p=1-q=\frac{1}{2}\) and as \(\mu+\sigma^2=3\) \(\Rightarrow \quad n p+n p q=3\)…