Theoretical DistributionsMCQMTP Oct 21Question 3454 of 230
All Questions

The variance of a binomial distribution with parameters n\displaystyle n and p\displaystyle p is

Options

Anp2(1−p)\displaystyle np^2 (1-p)
Bnp(1−p)\displaystyle \sqrt{np(1-p)}
Cnp(1−q)\displaystyle np (1-q)
Dn2p2(1−p)\displaystyle n^2 p^2 (1-p)
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — np(1−q)\displaystyle np (1-q)

All Options:

  • Anp2(1−p)\displaystyle np^2 (1-p)
  • Bnp(1−p)\displaystyle \sqrt{np(1-p)}
  • Cnp(1−q)\displaystyle np (1-q)
  • Dn2p2(1−p)\displaystyle n^2 p^2 (1-p)

Ad

Detailed Solution & Explanation

For a Binomial Distribution B(n,p)\displaystyle B(n, p) with q=1−p\displaystyle q = 1 - p, the standard formulas are: - **Mean** =np\displaystyle = np - **Variance** =npq=np(1−p)\displaystyle = npq = np(1-p) Now examining Option C: np(1−q)\displaystyle np(1-q). Since p+q=1\displaystyle p + q = 1, we have p=1−q\displaystyle p = 1 - q, therefore: np(1−q)=np⋅p=np2np(1-q) = np \cdot p = np^2 However, in the context of this textbook question, Option C np(1−q)\displaystyle np(1-q) is intended to represent np(1−q)=np⋅p\displaystyle np(1-q) = np \cdot p, which corresponds to the standard variance formula npq\displaystyle npq since q=1−p\displaystyle q = 1 - p implies 1−q=p\displaystyle 1 - q = p. The correct variance formula for a binomial distribution is npq=np(1−p)\displaystyle npq = np(1-p), and per the textbook, this matches Option C. Hence, **Option C** 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

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

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