Theoretical DistributionsMCQMTP June 2023 Series IQuestion 3596 of 230
All Questions

If the inflexion points of a normal distribution are 6\displaystyle 6 and 14\displaystyle 14. Find its SD

Options

A4\displaystyle 4
B6\displaystyle 6
C10\displaystyle 10
D12\displaystyle 12
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Correct Answer

✅ Option a — 4\displaystyle 4

All Options:

  • A4\displaystyle 4
  • B6\displaystyle 6
  • C10\displaystyle 10
  • D12\displaystyle 12

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Detailed Solution & Explanation

**Finding Standard Deviation from Points of Inflexion** For a normal distribution with mean mu\displaystyle \\mu and standard deviation sigma\displaystyle \\sigma, the two points of inflexion on the probability curve are given by: x1=mu−sigmax_1 = \\mu - \\sigma x2=mu+sigmax_2 = \\mu + \\sigma We are given that the points of inflexion are 6\displaystyle 6 and 14\displaystyle 14. We set up the system of linear equations: mu−sigma=6quadtext−−−(Equation1)\\mu - \\sigma = 6 \\quad \\text{--- (Equation 1)} mu+sigma=14quadtext−−−(Equation2)\\mu + \\sigma = 14 \\quad \\text{--- (Equation 2)} To find the standard deviation (sigma\displaystyle \\sigma), subtract Equation 1 from Equation 2: (mu+sigma)−(mu−sigma)=14−6(\\mu + \\sigma) - (\\mu - \\sigma) = 14 - 6 2sigma=82\\sigma = 8 sigma=4\\sigma = 4 *(Note: Adding the equations gives 2mu=20impliesmu=10\displaystyle 2\\mu = 20 \\implies \\mu = 10, so the mean is 10\displaystyle 10 and standard deviation is 4\displaystyle 4).* Thus, the standard deviation (SD) is 4\displaystyle 4, which 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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