Theoretical DistributionsMCQPYQ Dec 23Question 3554 of 230
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In a Standard Normal distribution, then the value of the mean(μ\displaystyle μ\displaystyle \mu) and SD (σ\displaystyle σ\displaystyle \sigma) is:

Select Your Answer (Keyboard: A, B, C, D)
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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

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=0μ=0\displaystyle \mu = 0 - The variance (and consequently the standard deviation) of the standard normal distribution is scaled to 1\displaystyle 1: σ2=1  ⟹  σ=1σ2=1\displaystyle \sigma^2 = 1 \implies σ=1\displaystyle \sigma = 1 Thus, for a standard normal distribution, the values of mean (μ\displaystyle μ\displaystyle \mu) and standard deviation (σ\displaystyle σ\displaystyle \sigma) are: μ=0andσ=1μ=0\displaystyle \mu = 0 \quad and\displaystyle \text{and} \quad σ=1\displaystyle \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.

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