Theoretical DistributionsMCQPYQ June 22Question 3425 of 230
All Questions

For a binomial distribution, there may be -

Options

AOne mode
BTwo mode
CMulti mode
DNo mode
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Correct Answer

✅ Option b — Two mode

All Options:

  • AOne mode
  • BTwo mode
  • CMulti mode
  • DNo mode

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Detailed Solution & Explanation

For a Binomial distribution B(n, p), the mode(s) depend on the value of (n+1)p:\n\nStep 1: Determine the condition for modes.\n- If (n+1)p is NOT an integer: the distribution has exactly ONE mode, which is the integer part of (n+1)p, i.e., \\lfloor(n+1)p\\rfloor.\n- If (n+1)p IS an integer: the distribution has TWO modes — (n+1)p and (n+1)p - 1.\n\nStep 2: Analyze what 'there may be' implies.\nThe question uses 'may have', implying it is asking what is POSSIBLE. Both one mode and two modes are possible depending on the parameters.\n\nStep 3: Focus on the special case.\nWhen (n+1)p is an integer, there are TWO modes. This is a valid and known property of the binomial distribution. So the distribution CAN have two modes.\n\nStep 4: Conclusion.\nThe binomial distribution may have two modes (when (n+1)p is an integer).\n\nHence, **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.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

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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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