Theoretical DistributionsPYQ Sept 25Question 4487 of 230
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If a binomial distribution has n=20\displaystyle n = 20 and p=0.3\displaystyle p = 0.3 what is its variance?

Options

A4.2
B5.6
C3.4
D2.9
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Correct Answer

✅ Option a — 4.2

All Options:

  • A4.2
  • B5.6
  • C3.4
  • D2.9

Detailed Solution & Explanation

For a binomial distribution B(n,p)\displaystyle B(n, p), the variance is given by the formula:
Variance=npq\text{Variance} = npq
where n\displaystyle n is the number of trials, p\displaystyle p is the probability of success, and q\displaystyle q is the probability of failure (q=1−p\displaystyle q = 1 - p).
1. **Given Data**:
- n=20\displaystyle n = 20
- p=0.3\displaystyle p = 0.3
2. **Calculate q\displaystyle q**:
q=1−p=1−0.3=0.7q = 1 - p = 1 - 0.3 = 0.7
3. **Calculate Variance**:
Variance=20×0.3×0.7\text{Variance} = 20 \times 0.3 \times 0.7
Variance=6×0.7=4.2\text{Variance} = 6 \times 0.7 = 4.2
Therefore, the variance of the binomial distribution is 4.2\displaystyle 4.2.
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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