Theoretical DistributionsPYQ May 25Question 4387 of 230
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If the points of inflexion of a normal curve are 6 and 14, then standard deviation of the distribution is

Options

A4
B8
C9.17
D32
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Correct Answer

✅ Option a — 4

All Options:

  • A4
  • B8
  • C9.17
  • D32

Detailed Solution & Explanation

For a normal distribution with mean μ\displaystyle \mu and standard deviation σ\displaystyle \sigma, the points of inflexion of the normal curve are located symmetrically about the mean at:
x1=μ−σx_1 = \mu - \sigma x2=μ+σx_2 = \mu + \sigma
We are given the points of inflexion as 6\displaystyle 6 and 14\displaystyle 14. Since x1<x2\displaystyle x_1 < x_2, we have:
μ−σ=6— (1)\mu - \sigma = 6 \quad \text{--- (1)} μ+σ=14— (2)\mu + \sigma = 14 \quad \text{--- (2)}
To find the standard deviation (σ\displaystyle \sigma), we subtract equation (1) from equation (2):
(μ+σ)−(μ−σ)=14−6(\mu + \sigma) - (\mu - \sigma) = 14 - 6 2σ=82\sigma = 8 σ=4\sigma = 4
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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