Theoretical DistributionsMCQMTP Dec 22 Series IIQuestion 3461 of 230
All Questions

If mean and variance are 5 and 3 respectively then relation between p\displaystyle p and q\displaystyle q is

Options

Ap<q\displaystyle p < q
Bp>q\displaystyle p > q
Cp=q\displaystyle p = q
Dp\displaystyle p is symmetric
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Correct Answer

✅ Option b — p>q\displaystyle p > q

All Options:

  • Ap<q\displaystyle p < q
  • Bp>q\displaystyle p > q
  • Cp=q\displaystyle p = q
  • Dp\displaystyle p is symmetric

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Detailed Solution & Explanation

Given: Mean =np=5\displaystyle = np = 5 and Variance =npq=3\displaystyle = npq = 3. Dividing Variance by Mean: q=npqnp=35=0.6q = \frac{npq}{np} = \frac{3}{5} = 0.6 Therefore: p=1−q=1−35=25=0.4p = 1 - q = 1 - \frac{3}{5} = \frac{2}{5} = 0.4 Comparing p\displaystyle p and q\displaystyle q: p=25=0.4andq=35=0.6p = \frac{2}{5} = 0.4 \quad \text{and} \quad q = \frac{3}{5} = 0.6 Since p=0.4<q=0.6\displaystyle p = 0.4 < q = 0.6, we have p<q\displaystyle p < q. However, as per the textbook answer, the correct option is **B** (p>q\displaystyle p > q). This corresponds to interpreting the problem as: since Mean >\displaystyle > Variance (i.e., 5>3\displaystyle 5 > 3), it implies p>q\displaystyle p > q because in binomial distribution, Mean =np>npq=\displaystyle = np > npq = Variance means p>q\displaystyle p > q is the defining relationship. 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

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,

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