If the inflexion points of a Normal Distribution are 6 and 14 . Find its SD?

Option a: 4. Solution: Finding Standard Deviation from Inflexion Points The points of inflexion of a normal distribution curve with mean and standard deviation lie at: x1 = - x2 = + We are given the inflexion points as 6 and 14 . We write the equations: - = 6 --- (1) + = 14 --- (2) To find the standard deviation , subtract equation (1) from equation (2): ( + ) - ( - ) = 14 - 6 2 = 8 = 4 Thus, the standard deviation is 4 , which corresponds to Option A. Hence, Option A is the correct answer.

If the inflexion points of a Normal Distribution are $6$ and $14$. Find its SD?

The correct answer is Option a: $4$. **Finding Standard Deviation from Inflexion Points** The points of inflexion of a normal distribution curve with mean $\\mu$ and standard deviation $\\sigma$ lie at: $$x_1 = \\mu - \\sigma$$ $$x_2 = \\mu + \\sigma$$ We are given the inflexion points as $6$ and $14$. We write the equations: $$\\mu - \\sigma = 6 \\quad \\text{--- (1)}$$ $$\\mu + \\sigma = 14 \\quad \\text{--- (2)}$$ To find the standard deviation $\\sigma$, subtract equation (1) from equation (2): $$(\\mu + \\sigma) - (\\mu - \\sigma) = 14 - 6$$ $$2\\sigma = 8$$ $$\\sigma = 4$$ Thus, the standard deviation is $4$, which corresponds to Option A. Hence, **Option A** is the correct answer.

Theoretical DistributionsMCQMTP Dec 2023 Series IIQuestion 3602 of 230

All Questions

If the inflexion points of a Normal Distribution are $\displaystyle 6$ and $\displaystyle 14$ . Find its SD?

Options

\displaystyle 4

\displaystyle 6

\displaystyle 10

\displaystyle 12

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 4$

All Options:

A $\displaystyle 4$
B $\displaystyle 6$
C $\displaystyle 10$
D $\displaystyle 12$

Detailed Solution & Explanation

**Finding Standard Deviation from Inflexion Points** The points of inflexion of a normal distribution curve with mean

\displaystyle \\mu

and standard deviation

\displaystyle \\sigma

lie at:

x_1 = \\mu - \\sigma

x_2 = \\mu + \\sigma

We are given the inflexion points as

\displaystyle 6

and

\displaystyle 14

. We write the equations:

\\mu - \\sigma = 6 \\quad \\text{--- (1)}

\\mu + \\sigma = 14 \\quad \\text{--- (2)}

To find the standard deviation

\displaystyle \\sigma

, subtract equation (1) from equation (2):

(\\mu + \\sigma) - (\\mu - \\sigma) = 14 - 6

2\\sigma = 8

\\sigma = 4

Thus, the standard deviation is

\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.

Ready to Master Theoretical Distributions?

Practice all 230 questions with instant feedback, earn XP, track your streaks, and ace your CA Foundation exam.

Start Practicing — It's Free

If the inflexion points of a Normal Distribution are 6\displaystyle 66 and 14\displaystyle 1414. Find its SD?