Option a: 99.73%. Solution: Area Under Normal Curve Within ± 3sigma For a normal distribution with mean mu and standard deviation sigma , the probability distribution is perfectly symmetric about the mean. According to the empirical rule (68-95-99.7 rule) for a normal distribution: 1. The area under the curve within one standard deviation of the mean ( mu ± 1sigma ) is approximately 68.27% . 2. The area under the curve within two standard deviations of the mean ( mu ± 2sigma ) is approximately 95.45% . 3. The area under the curve within three standard deviations of the mean ( mu ± 3sigma ) is approximately 99.73% . Mathematically, this is expressed as: P(mu - 3sigma ≤ X ≤ mu + 3sigma) ≈ 0.9973 Thus, the percentage of the area under the normal curve covered by ± 3sigma is 99.73% . Hence, Option A is the correct answer.

Area under $\pm 3\sigma$

The correct answer is Option a: 99.73%. **Area Under Normal Curve Within $\pm 3\sigma$** For a normal distribution with mean $\mu$ and standard deviation $\sigma$, the probability distribution is perfectly symmetric about the mean. According to the empirical rule (68-95-99.7 rule) for a normal distribution: 1. The area under the curve within one standard deviation of the mean ($\mu \pm 1\sigma$) is approximately $68.27\%$. 2. The area under the curve within two standard deviations of the mean ($\mu \pm 2\sigma$) is approximately $95.45\%$. 3. The area under the curve within three standard deviations of the mean ($\mu \pm 3\sigma$) is approximately $99.73\%$. Mathematically, this is expressed as: $$P(\mu - 3\sigma \le X \le \mu + 3\sigma) \approx 0.9973$$ Thus, the percentage of the area under the normal curve covered by $\pm 3\sigma$ is $99.73\%$. Hence, **Option A** is the correct answer.

Theoretical DistributionsMCQPYQ Nov. 19Question 3543 of 230

All Questions

Area under $\displaystyle \pm 3\sigma$

Options

A99.73%

B99%

C100%

D99.37%

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Correct Answer

✅ Option a — 99.73%

All Options:

A99.73%
B99%
C100%
D99.37%

Detailed Solution & Explanation

**Area Under Normal Curve Within

\displaystyle \pm 3\sigma

** For a normal distribution with mean

\displaystyle \mu

and standard deviation

\displaystyle \sigma

, the probability distribution is perfectly symmetric about the mean. According to the empirical rule (68-95-99.7 rule) for a normal distribution: 1. The area under the curve within one standard deviation of the mean (

\displaystyle \mu \pm 1\sigma

) is approximately

\displaystyle 68.27\%

. 2. The area under the curve within two standard deviations of the mean (

\displaystyle \mu \pm 2\sigma

) is approximately

\displaystyle 95.45\%

. 3. The area under the curve within three standard deviations of the mean (

\displaystyle \mu \pm 3\sigma

) is approximately

\displaystyle 99.73\%

. Mathematically, this is expressed as:

P(\mu - 3\sigma \le X \le \mu + 3\sigma) \approx 0.9973

Thus, the percentage of the area under the normal curve covered by

\displaystyle \pm 3\sigma

\displaystyle 99.73\%

. 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.

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Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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Area under ±3σ\displaystyle \pm 3\sigma±3σ

Options

Correct Answer

All Options:

Detailed Solution & Explanation

About This Chapter: Theoretical Distributions

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Area under $\displaystyle \pm 3\sigma$