When ' p ' is large than 0.5 , the Binomial Distribution is

Option a: Asymmetrical. Solution: Key Properties of Binomial Distribution regarding Skewness: - When p = 0.5: The distribution is symmetrical. - When p ≠ 0.5: The distribution is asymmetrical (skewed). - When p 0.5: Negatively skewed (skewed to the left). Skewness of Binomial distribution: Skewness = q - p/sqrt(npq) When p > 0.5, then q < p, so (q - p) < 0, meaning the distribution is negatively skewed, hence asymmetrical. Hence, Option A is the correct answer.

When '$p$' is large than $0.5$, the Binomial Distribution is

The correct answer is Option a: Asymmetrical. **Key Properties of Binomial Distribution regarding Skewness:** - When **p = 0.5**: The distribution is **symmetrical**. - When **p ≠ 0.5**: The distribution is **asymmetrical** (skewed). - When p 0.5: Negatively skewed (skewed to the left). **Skewness of Binomial distribution:** $$\text{Skewness} = \frac{q - p}{\sqrt{npq}}$$ When p > 0.5, then q < p, so (q - p) < 0, meaning the distribution is **negatively skewed**, hence **asymmetrical**. Hence, **Option A** is the correct answer.

Theoretical DistributionsMCQMTP Dec 2023 Series IQuestion 3466 of 230

All Questions

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

Options

AAsymmetrical

BSymmetrical

CBoth

DNone of these

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Correct Answer

✅ Option a — Asymmetrical

All Options:

AAsymmetrical
BSymmetrical
CBoth
DNone of these

Detailed Solution & Explanation

**Key Properties of Binomial Distribution regarding Skewness:** - When **p = 0.5**: The distribution is **symmetrical**. - When **p ≠ 0.5**: The distribution is **asymmetrical** (skewed). - When p < 0.5: Positively skewed (skewed to the right). - When p > 0.5: Negatively skewed (skewed to the left). **Skewness of Binomial distribution:**

\text{Skewness} = \frac{q - p}{\sqrt{npq}}

When p > 0.5, then q < p, so (q - p) < 0, meaning the distribution is **negatively skewed**, hence **asymmetrical**. Hence, **Option A** 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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When 'p\displaystyle pp' is large than 0.5\displaystyle 0.50.5, the Binomial Distribution is