Theoretical DistributionsMCQMTP Nov 18Question 3437 of 230
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If p\displaystyle p is increased for a fixed n\displaystyle n; the Binomial distribution shifts to the

Options

ARight
BLeft
CAbove
DBelow
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Correct Answer

✅ Option a — Right

All Options:

  • ARight
  • BLeft
  • CAbove
  • DBelow

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Detailed Solution & Explanation

**Effect of Increasing p on Binomial Distribution Shape**\n\nFor a Binomial Distribution B(n,p)\displaystyle B(n, p) with fixed n\displaystyle n:\ntextMean=np\\text{Mean} = np\n\n**When p increases (for fixed n):**\n- Mean =np\displaystyle = np **increases**\n- The distribution is centered at a higher value\n- The distribution shifts to the **right** on the number line\n\n**Intuition:**\n- If p=0.1\displaystyle p = 0.1: Mean =0.1n\displaystyle = 0.1n (distribution concentrated near 0, skewed right)\n- If p=0.5\displaystyle p = 0.5: Mean =0.5n\displaystyle = 0.5n (symmetric, centered in middle)\n- If p=0.9\displaystyle p = 0.9: Mean =0.9n\displaystyle = 0.9n (distribution concentrated near n\displaystyle n, shifted far right)\n\nAs p\displaystyle p increases from 0 to 1, the peak of the distribution moves from left to right.\n\nHence, **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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For a Poisson distribution,

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