Theoretical DistributionsMCQMTP May 19Question 3438 of 230
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A binomial distribution is

Options

Anever symmetrical
Bnever positively skewed
Cnever negatively skewed.
Dsymmetrical when p=0.5\displaystyle p = 0.5.
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Correct Answer

✅ Option d — symmetrical when p=0.5\displaystyle p = 0.5.

All Options:

  • Anever symmetrical
  • Bnever positively skewed
  • Cnever negatively skewed.
  • Dsymmetrical when p=0.5\displaystyle p = 0.5.

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Detailed Solution & Explanation

**Symmetry of Binomial Distribution**\n\nThe skewness of a Binomial Distribution B(n,p)\displaystyle B(n, p) depends on p\displaystyle p:\ntextSkewness=fracq−psqrtnpq=frac1−2psqrtnpq\\text{Skewness} = \\frac{q - p}{\\sqrt{npq}} = \\frac{1 - 2p}{\\sqrt{npq}}\n\n**Three cases:**\n\n| Condition | Skewness | Shape |\n|-----------|----------|-------|\n| p<0.5\displaystyle p < 0.5 | >0\displaystyle > 0 (positive) | Positively skewed (right-skewed) |\n| p=0.5\displaystyle p = 0.5 | =0\displaystyle = 0 | **Symmetrical** |\n| p>0.5\displaystyle p > 0.5 | <0\displaystyle < 0 (negative) | Negatively skewed (left-skewed) |\n\n**Analysis of options:**\n- (a) Incorrect — it IS symmetrical when p=0.5\displaystyle p = 0.5\n- (b) Incorrect — it CAN be positively skewed when p<0.5\displaystyle p < 0.5\n- (c) Incorrect — it CAN be negatively skewed when p>0.5\displaystyle p > 0.5\n- (d) **Correct** — Binomial distribution is symmetrical when p=0.5\displaystyle p = 0.5\n\nHence, **Option D** 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.

More Questions from Theoretical Distributions

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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,

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