Theoretical DistributionsMCQMTP May 18Question 3432 of 230
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When 'p\displaystyle p' =0.5\displaystyle = 0.5, the

Options

AAsymmetrical.
BSymmetrical
CBoth of above.
DNone of these
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Correct Answer

✅ Option b — Symmetrical

All Options:

  • AAsymmetrical.
  • BSymmetrical
  • CBoth of above.
  • DNone of these

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Detailed Solution & Explanation

ForaBinomialdistributionB(n,p),theskewnessisdeterminedbythevalueofp:\n\nStep1:Recalltheskewnessformulaforbinomialdistribution.\nSkewness=fracq−psqrtnpq\n\nStep2:Substitutep=0.5andq=0.5.\nSkewness=frac0.5−0.5sqrtnpq=frac0sqrtnpq=0\n\nStep3:Interprettheresult.\n−Skewness=0meansthedistributionisperfectlysymmetrical.\n−Whenp=q=0.5,thedistributionissymmetricaboutitsmean.\n\nStep4:AdditionalAnalysis.\n−Ifp<0.5(i.e.,p<q):distributionispositivelyskewed.\n−Ifp>0.5(i.e.,p>q):distributionisnegativelyskewed.\n−Ifp=0.5(i.e.,p=q):distributionissymmetrical.\n\nTherefore,whenp=0.5,thebinomialdistributionissymmetrical.\n\nHence,∗∗OptionB∗∗isthecorrectanswer.\displaystyle For a Binomial distribution B(n, p), the skewness is determined by the value of p:\n\nStep 1: Recall the skewness formula for binomial distribution.\nSkewness = \\frac{q - p}{\\sqrt{npq}}\n\nStep 2: Substitute p = 0.5 and q = 0.5.\nSkewness = \\frac{0.5 - 0.5}{\\sqrt{npq}} = \\frac{0}{\\sqrt{npq}} = 0\n\nStep 3: Interpret the result.\n- Skewness = 0 means the distribution is perfectly symmetrical.\n- When p = q = 0.5, the distribution is symmetric about its mean.\n\nStep 4: Additional Analysis.\n- If p < 0.5 (i.e., p < q): distribution is positively skewed.\n- If p > 0.5 (i.e., p > q): distribution is negatively skewed.\n- If p = 0.5 (i.e., p = q): distribution is symmetrical.\n\nTherefore, when p = 0.5, the binomial distribution is symmetrical.\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.

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For a Poisson distribution,

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