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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

In a binomial distribution, if the mean is 6 and the standard...

In a binomial distribution, if the mean is 6 and the standard deviation is 2,thenwhatarethevaluesoftheparameters\sqrt{2}, then what are the values of the parametersnandandprespectively?respectively?

Options

  1. A18and1318 and \frac{1}{3}
  2. B9and139 and \frac{1}{3}
  3. C18and2318 and \frac{2}{3}
  4. D9and239 and \frac{2}{3}

Correct answer

D. 9and239 and \frac{2}{3}

Step-by-step solution

Given that, mean xˉ=np=6\bar{x}=n p=6 and S.D =npq=2⇒npq=2=\sqrt{\mathrm{npq}}=\sqrt{2} \Rightarrow \mathrm{npq}=2 Divide (ii) by (i), we get npqnp=26⇒q=13\frac{\mathrm{npq}}{\mathrm{np}}=\frac{2}{6} \Rightarrow \mathrm{q}=\frac{1}{3} We know that p=1−q=1−13=23∴P=23\mathrm{p}=1-\mathrm{q}=1-\frac{1}{3}=\frac{2}{3}\therefore \quad \mathrm{P}=\frac{2}{3} Put the value of pp in (i), we get n×23=6n=9\begin{aligned} & \mathrm{n} \times \frac{2}{3}=6 \\ & \mathrm{n}=9 \end{aligned}
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