Theoretical DistributionsMTP June 2023 Series IQuestion 3992 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

Detailed Solution & Explanation

**Standard Normal Distribution Standard Deviation**\n\nA normal distribution with mean mu\displaystyle \\mu and standard deviation sigma\displaystyle \\sigma is denoted by N(mu,sigma2)\displaystyle N(\\mu, \\sigma^2).\n\nA **standard normal distribution** is a special case of the normal distribution where:\n- The mean (mu\displaystyle \\mu) is 0\displaystyle 0.\n- The standard deviation (sigma\displaystyle \\sigma) is 1\displaystyle 1.\n- The variance (sigma2\displaystyle \\sigma^2) is 12=1\displaystyle 1^2 = 1.\n\nA standard normal random variable is typically denoted by Z\displaystyle Z, where:\nZ=fracX−musigmaZ = \\frac{X - \\mu}{\\sigma}\nAnd:\nZsimN(0,1)Z \\sim N(0, 1)\n\nTherefore, for a continuous random variable following standard normal distribution, the value of standard deviation is exactly 1\displaystyle 1.\n\nHence, **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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