Theoretical DistributionsMCQMTP Dec 2023 Series IQuestion 3465 of 230
All Questions

If x\displaystyle x is binomial with parameter 15\displaystyle 15 and 13\displaystyle \frac{1}{3}, what is mode of the distribution?

Options

A5\displaystyle 5 and 6\displaystyle 6
B5\displaystyle 5
C5.50\displaystyle 5.50
D6\displaystyle 6
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Correct Answer

Option b5\displaystyle 5

All Options:

  • A5\displaystyle 5 and 6\displaystyle 6
  • B5\displaystyle 5
  • C5.50\displaystyle 5.50
  • D6\displaystyle 6

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Detailed Solution & Explanation

**Given:** - n = 15 - p = 1/3 **Finding Mode of Binomial Distribution:** Compute (n + 1)p: (n+1)p=(15+1)×13=16×13=1635.33(n+1)p = (15+1) \times \frac{1}{3} = 16 \times \frac{1}{3} = \frac{16}{3} \approx 5.33 Since (n+1)p = 5.33 is **not an integer**, the distribution has a **unique mode**: Mode=(n+1)p=5.33=5\text{Mode} = \lfloor (n+1)p \rfloor = \lfloor 5.33 \rfloor = 5 **Note:** If (n+1)p were an integer, there would be two modes. Since it is not, mode = 5 only. 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

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