Theoretical DistributionsMCQPYQ July 21Question 3423 of 230
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If X\displaystyle X is a binomial variate with p=1/3\displaystyle p = 1/3, for the experiment of $90$ trials, then the standard deviation is equal to:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c —

25\displaystyle 2\sqrt{5}

All Options:

  • A
    −5\displaystyle -\sqrt{5}
  • B
    5\displaystyle \sqrt{5}
  • C
    25\displaystyle 2\sqrt{5}
  • D
    15\displaystyle \sqrt{15}

Detailed Solution & Explanation

Given: X ~ B(n, p) where n = 90 and p = 1/3.\n\nStep 1: Find q.\nq = 1 - p = 1 - \13\displaystyle \frac{1}{3} = \23\displaystyle \frac{2}{3}\n\nStep 2: Apply the formula for Standard Deviation.\nSD = \npq\displaystyle \sqrt{npq}\n\nStep 3: Substitute the values.\nSD = \90timesfrac13timesfrac23\displaystyle \sqrt{90 \\times \\frac{1}{3} \\times \\frac{2}{3}}\n\nStep 4: Simplify inside the square root.\n= \90timesfrac29\displaystyle \sqrt{90 \\times \\frac{2}{9}}\n= \frac1809\displaystyle \sqrt{\\frac{180}{9}}\n= \20\displaystyle \sqrt{20}\n\nStep 5: Simplify \20\displaystyle \sqrt{20}.\n\20\displaystyle \sqrt{20} = \4times5=2\displaystyle \sqrt{4 \\times 5} = 2\5\displaystyle \sqrt{5}\n\nTherefore, SD = 2\5\displaystyle \sqrt{5}.\n\nHence, **Option C** is the correct answer.

About This Chapter: Theoretical Distributions

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Binomial, Poisson, Normal Distribution

This chapter covers Binomial, Poisson, Normal Distribution and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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For a Poisson distribution,

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