Theoretical DistributionsMCQMTP Dec 2022 Series IIQuestion 3542 of 230
All Questions

If the points of inflexion of a normal curve are 40\displaystyle 40 & 60\displaystyle 60 respectively, then mean deviation is:

Options

A8\displaystyle 8
B45\displaystyle 45
C50\displaystyle 50
D60\displaystyle 60
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Correct Answer

✅ Option a — 8\displaystyle 8

All Options:

  • A8\displaystyle 8
  • B45\displaystyle 45
  • C50\displaystyle 50
  • D60\displaystyle 60

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Detailed Solution & Explanation

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