Theoretical DistributionsMTP June 2023 Series IQuestion 3993 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

Detailed Solution & Explanation

**Points of Inflexion of a Normal Distribution**\n\nFor a normal distribution with mean mu\displaystyle \\mu and standard deviation sigma\displaystyle \\sigma, the probability density function is symmetric about x=mu\displaystyle x = \\mu and has a bell shape.\n\nThe **points of inflexion** of the normal curve (where the curvature changes direction) are located at a distance of one standard deviation on either side of the mean.\nMathematically, they are:\nx1=mu−sigmax_1 = \\mu - \\sigma\nx2=mu+sigmax_2 = \\mu + \\sigma\n\nGiven:\n- Lower point of inflexion = 6\displaystyle 6\n- Upper point of inflexion = 14\displaystyle 14\n\nWe can write the system of equations:\n1) mu−sigma=6\displaystyle \\mu - \\sigma = 6\n2) mu+sigma=14\displaystyle \\mu + \\sigma = 14\n\nSubtracting equation (1) from equation (2):\n(mu+sigma)−(mu−sigma)=14−6(\\mu + \\sigma) - (\\mu - \\sigma) = 14 - 6\n2sigma=82\\sigma = 8\nsigma=frac82=4\\sigma = \\frac{8}{2} = 4\n\nThus, the standard deviation (SD) of the distribution is 4\displaystyle 4.\n\nHence, **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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