Theoretical DistributionsMCQMTP May 19Question 3565 of 230
All Questions

The total area of the normal curve is

Options

AOne
B50 percent
C0.50
DAny value between 0 and 1
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Correct Answer

✅ Option a — One

All Options:

  • AOne
  • B50 percent
  • C0.50
  • DAny value between 0 and 1

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Detailed Solution & Explanation

**Total Area of Normal Curve** The normal distribution is a continuous probability distribution. **First Principles:** By definition, for any continuous probability density function f(x)\displaystyle f(x), the total area under the curve (representing the sum of all probabilities) is always equal to 1: ∫−∞∞f(x) dx=1\int_{-\infty}^{\infty} f(x)\,dx = 1 Thus, the total area of the normal curve is exactly **One**. **Evaluating Options:** - **Option A (One):** Correct, the total area is 1\displaystyle 1. - **Option B (50 percent) & Option C (0.50):** Represent the area under only one half of the symmetric curve (either left of the mean or right of the mean). 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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A random variable X\displaystyle X follows Binomial Distribution With E(x)=2\displaystyle E(x)=2 and V(x)=1.2\displaystyle V(x)=1.2, then the value of n\displaystyle n is

When 'p\displaystyle p' is large than 0.5\displaystyle 0.5, the Binomial Distribution is:

For a Poisson distribution,

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