Theoretical DistributionsMTP May 19 Series IIQuestion 3981 of 230
All Questions

If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is

Options

A8
B45
C50
D60
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Correct Answer

✅ Option a — 8

All Options:

  • A8
  • B45
  • C50
  • D60

Detailed Solution & Explanation

**Parameters from Points of Inflexion** The points of inflexion of a normal curve with mean μ\displaystyle \mu and standard deviation σ\displaystyle \sigma 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 1: Solve for parameters μ\displaystyle \mu and σ\displaystyle \sigma** - Adding Equations 1 and 2: 2μ=100  ⟹  μ=502\mu = 100 \implies \mu = 50 - Subtracting Equation 1 from Equation 2: 2σ=20  ⟹  σ=102\sigma = 20 \implies \sigma = 10 **Step 2: Calculate Mean Deviation (MD)** The Mean Deviation (MD) of a normal distribution is given by: MD≈0.8σMD \approx 0.8\sigma Substitute σ=10\displaystyle \sigma = 10: MD=0.8×10=8MD = 0.8 \times 10 = 8 **Step 3: Analyze the options** - The calculated Mean Deviation is 8\displaystyle 8 (Option A). - The textbook lists Option C (50\displaystyle 50) as correct, which corresponds to the value of the **mean** (μ\displaystyle \mu). This indicates a typo in the question text where "mean" was mistakenly printed as "mean deviation". - For the question as written, the correct answer is 8\displaystyle 8. 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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For a Poisson distribution,

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