Theoretical DistributionsMCQPYQ Dec 23Question 3554 of 230
All Questions

In a Standard Normal distribution, then the value of the mean(μ\displaystyle \mu) and SD (σ\displaystyle \sigma) is:

Options

Aμ=0,σ=0\displaystyle \mu = 0, \sigma = 0
Bμ=0,σ=1\displaystyle \mu = 0, \sigma = 1
Cμ=1,σ=0\displaystyle \mu = 1, \sigma = 0
Dμ=1,σ=1\displaystyle \mu = 1, \sigma = 1
For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option b — μ=0,σ=1\displaystyle \mu = 0, \sigma = 1

All Options:

  • Aμ=0,σ=0\displaystyle \mu = 0, \sigma = 0
  • Bμ=0,σ=1\displaystyle \mu = 0, \sigma = 1
  • Cμ=1,σ=0\displaystyle \mu = 1, \sigma = 0
  • Dμ=1,σ=1\displaystyle \mu = 1, \sigma = 1

Ad

Detailed Solution & Explanation

**Parameters of a Standard Normal Distribution** The standard normal distribution is a special case of the normal distribution where the random variable is standardized. - The standard normal random variable is typically denoted by Z\displaystyle Z. - By definition, the mean (expected value) of the standard normal distribution is scaled to 0\displaystyle 0: μ=0\mu = 0 - The variance (and consequently the standard deviation) of the standard normal distribution is scaled to 1\displaystyle 1: σ2=1  ⟹  σ=1\sigma^2 = 1 \implies \sigma = 1 Thus, for a standard normal distribution, the values of mean (μ\displaystyle \mu) and standard deviation (σ\displaystyle \sigma) are: μ=0andσ=1\mu = 0 \quad \text{and} \quad \sigma = 1 Hence, **Option B** 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.

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