Theoretical DistributionsMCQPYQ Dec 22Question 3426 of 230
All Questions

The standard deviation of binomial distribution is:

Options

Anpq\displaystyle npq
Bnpq\displaystyle \sqrt{npq}
Cnp\displaystyle np
Dnp\displaystyle \sqrt{np}
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — npq\displaystyle \sqrt{npq}

All Options:

  • Anpq\displaystyle npq
  • Bnpq\displaystyle \sqrt{npq}
  • Cnp\displaystyle np
  • Dnp\displaystyle \sqrt{np}

Ad

Detailed Solution & Explanation

ForaBinomialdistributionX B(n,p):\n\nStep1:Recallthekeyformulas.\n−Mean=np\n−Variance=npq\n−StandardDeviation=sqrttextVariance\n\nStep2:ComputetheStandardDeviation.\nSD=sqrtnpq\n\nwhere:\n−n=numberoftrials\n−p=probabilityofsuccess\n−q=1−p=probabilityoffailure\n\nStep3:Matchwithoptions.\nOptionA:np—thisistheMean,notSD.\nOptionB:sqrtnpq—thisistheStandardDeviation.✓\nOptionC:npq—thisistheVariance,notSD.\nOptionD:sqrtnp—thisisincorrect.\n\nHence,∗∗OptionB∗∗isthecorrectanswer.\displaystyle For a Binomial distribution X ~ B(n, p):\n\nStep 1: Recall the key formulas.\n- Mean = np\n- Variance = npq\n- Standard Deviation = \\sqrt{\\text{Variance}}\n\nStep 2: Compute the Standard Deviation.\nSD = \\sqrt{npq}\n\nwhere:\n- n = number of trials\n- p = probability of success\n- q = 1 - p = probability of failure\n\nStep 3: Match with options.\nOption A: np — this is the Mean, not SD.\nOption B: \\sqrt{npq} — this is the Standard Deviation. ✓\nOption C: npq — this is the Variance, not SD.\nOption D: \\sqrt{np} — this is incorrect.\n\nHence, **Option B** 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.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free