Theoretical DistributionsMCQMTP June 22Question 3590 of 230
All Questions

The variance of standard normal distribution

Options

A1
B0
Cσ2\displaystyle \sigma^2
D0
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — 1

All Options:

  • A1
  • B0
  • Cσ2\displaystyle \sigma^2
  • D0

Ad

Detailed Solution & Explanation

**Variance of Standard Normal Distribution** **First Principles:** A standard normal distribution (typically denoted by Z\displaystyle Z) is a normal distribution scaled to have standardized parameters: 1. The mean is centered at zero: μ=0\mu = 0 2. The standard deviation is scaled to one: σ=1\sigma = 1 3. The variance is defined as the square of standard deviation: Variance=σ2=12=1\text{Variance} = \sigma^2 = 1^2 = 1 Thus, the variance of the standard normal distribution is 1\displaystyle 1. This matches 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.

Key Concepts to Understand

Variance

A measure of dispersion equal to the average of the squared deviations of each data point from the mean. Formula: σ² = Σ(xᵢ − x̄)² / n. Standard Deviation = √Variance.

More Questions from Theoretical Distributions

Find the variance of binomial distribution with n=10\displaystyle n=10, p=0.3\displaystyle p=0.3

When p=0.5\displaystyle p=0.5, the binomial distribution is

If mean and standard deviation of a binomial distribution is 10\displaystyle 10 and 2\displaystyle 2 respectively, q\displaystyle q will be

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,

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