Theoretical DistributionsMCQMTP Dec 2022 Series IIQuestion 3542 of 230
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If the points of inflexion of a normal curve are $40\displaystyle & $60 respectively, then mean deviation is:

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — 8\displaystyle 8

All Options:

  • A8\displaystyle 8
  • B$45$
  • C$50$
  • D$60$

Detailed Solution & Explanation

**Mean Deviation of Normal Distribution from Points of Inflexion** **Given:** - Points of inflexion of the normal curve are $40\displaystyle and $60. **Step 1: Relate points of inflexion to parameters mu\displaystyle \μ\displaystyle \mu and sigma\displaystyle \σ\displaystyle \sigma** For any normal distribution, the points of inflexion are equidistant from the mean mu\displaystyle \μ\displaystyle \mu at a distance of one standard deviation sigma\displaystyle \σ\displaystyle \sigma: textPointofInflexion1=mu−sigma=40\Point of Inflexion 1\displaystyle \text{Point of Inflexion 1} = \μ\displaystyle \mu - \σ=40\displaystyle \sigma = 40 textPointofInflexion2=mu+sigma=60\Point of Inflexion 2\displaystyle \text{Point of Inflexion 2} = \μ\displaystyle \mu + \σ=60\displaystyle \sigma = 60 **Step 2: Solve for sigma\displaystyle \σ\displaystyle \sigma** Subtract the first equation from the second equation: (mu+sigma)−(mu−sigma)=60−40(\μ\displaystyle \mu + \σ\displaystyle \sigma) - (\μ\displaystyle \mu - \σ\displaystyle \sigma) = 60 - 40 2sigma=20impliessigma=102\σ=20\displaystyle \sigma = 20 \\implies \σ=10\displaystyle \sigma = 10 **Step 3: Calculate Mean Deviation (M.D.)** For a normal distribution, the relationship between Mean Deviation about mean and Standard Deviation sigma\displaystyle \σ\displaystyle \sigma is: textMeanDeviationapprox0.8sigma=frac45sigma\Mean Deviation\displaystyle \text{Mean Deviation} \≈\displaystyle \approx 0.8 \σ\displaystyle \sigma = \45\displaystyle \frac{4}{5} \σ\displaystyle \sigma Substitute sigma=10\displaystyle \σ=10\displaystyle \sigma = 10: textMeanDeviation=0.8times10=8\Mean Deviation=0\displaystyle \text{Mean Deviation} = 0.8 \×\displaystyle \times 10 = 8 This corresponds to 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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