Theoretical DistributionsMCQPYQ Nov 20Question 3421 of 230
All Questions

If the probability of success in a binomial distribution is less than one-half, then the binomial distribution

Options

Ais skewed to left
Bis skewed to right
Chas two modes
Dhas median at a point >\displaystyle > mean +1/2\displaystyle + 1/2
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — is skewed to right

All Options:

  • Ais skewed to left
  • Bis skewed to right
  • Chas two modes
  • Dhas median at a point >\displaystyle > mean +1/2\displaystyle + 1/2

Ad

Detailed Solution & Explanation

**Skewness of Binomial Distribution when p<frac12\displaystyle p < \\frac{1}{2}** **Key property:** The skewness of a binomial distribution depends on the value of p\displaystyle p: Skewness (coefficient)=fracq−psqrtnpq\text{Skewness (coefficient)} = \\frac{q - p}{\\sqrt{npq}} **Case: p<frac12\displaystyle p < \\frac{1}{2}** If p<frac12\displaystyle p < \\frac{1}{2}, then q=1−p>frac12\displaystyle q = 1 - p > \\frac{1}{2}, which means q>p\displaystyle q > p. Therefore: q−p>0\displaystyle q - p > 0, so the skewness coefficient is **positive**. **Positive skewness** means the distribution is **skewed to the right** (right-tailed), i.e., the tail is longer on the right side. **Intuition:** When p<frac12\displaystyle p < \\frac{1}{2}, successes are rare, so most values cluster near 0 (low end), with a long tail stretching towards n\displaystyle n (high end) → **right skew**. **Summary of skewness rules for binomial:** - p<0.5\displaystyle p < 0.5: Positively skewed (skewed to the **right**) ✓ - p=0.5\displaystyle p = 0.5: Symmetric (no skew) - p>0.5\displaystyle p > 0.5: Negatively skewed (skewed to the **left**) Hence, **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

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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