Theoretical DistributionsMCQMTP June 2023 Series IQuestion 3595 of 230
All Questions

For a continuous random variable following standard normal distribution, what is the value of standard deviation?

Options

A1\displaystyle 1
B0\displaystyle 0
C−1\displaystyle -1
DMore than 1\displaystyle 1
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Correct Answer

✅ Option a — 1\displaystyle 1

All Options:

  • A1\displaystyle 1
  • B0\displaystyle 0
  • C−1\displaystyle -1
  • DMore than 1\displaystyle 1

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Detailed Solution & Explanation

**Standard Deviation of Standard Normal Distribution** By definition, the standard normal distribution is a normalized version of the general normal distribution where: - The mean (mu\displaystyle \\mu) is shifted to 0\displaystyle 0. - The standard deviation (sigma\displaystyle \\sigma) is scaled to 1\displaystyle 1. Thus, a standard normal variable Z\displaystyle Z has parameters ZsimN(mu=0,sigma2=12)\displaystyle Z \\sim N(\\mu = 0, \\sigma^2 = 1^2). Therefore, the standard deviation is exactly 1\displaystyle 1, 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.

Key Concepts to Understand

Standard Deviation

A measure of the dispersion or spread of values in a data set around the mean. It is the square root of Variance. A lower standard deviation indicates data points are clustered close to the mean; a higher value indicates greater spread.

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