Theoretical DistributionsMCQMTP May 19Question 3570 of 230
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If the points of inflexion of a normal curve are 40 & 60 respectively, then its mean deviation

Options

A8
B45
C
D
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Correct Answer

✅ Option a — 8

All Options:

  • A8
  • B45
  • C
  • D

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Detailed Solution & Explanation

**Mean Deviation from Points of Inflexion** **Step 1: Express points of inflexion in terms of parameters** For a normal curve with mean μ\displaystyle \mu and standard deviation σ\displaystyle \sigma, the points of inflexion are: x1=μ−σx_1 = \mu - \sigma x2=μ+σx_2 = \mu + \sigma Given the points of inflexion are 40\displaystyle 40 and 60\displaystyle 60: μ−σ=40— (Equation 1)\mu - \sigma = 40 \quad \text{--- (Equation 1)} μ+σ=60— (Equation 2)\mu + \sigma = 60 \quad \text{--- (Equation 2)} **Step 2: Solve for standard deviation σ\displaystyle \sigma** Subtract Equation 1 from Equation 2: (μ+σ)−(μ−σ)=60−40(\mu + \sigma) - (\mu - \sigma) = 60 - 40 2σ=20  ⟹  σ=102\sigma = 20 \implies \sigma = 10 **Step 3: Calculate Mean Deviation (MD)** In a normal distribution, the Mean Deviation is related to σ\displaystyle \sigma by: MD≈0.8σMD \approx 0.8\sigma Substitute σ=10\displaystyle \sigma = 10: MD=0.8×10=8MD = 0.8 \times 10 = 8 This matches Option A. Hence, **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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