If the distribution of normal variable is shown as N(20, 4) then which of the following intervals includes 99.

Question 22 of 46

N(20, 4)

(a)

(18, 22)

(b)

(16, 24)

(c)

(14, 26)

(d)

(12, 28)

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022MCQ· 1mImportance★★★★★

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With $\mu=20$ , $\sigma=\sqrt{4}=2$ , the interval covering $99.73\%$ is $\mu\pm 3\sigma = 20\pm 6 = \mathbf{(14,26)}$ .

Given: $N(20,4)$ means mean $\mu=20$ and variance $\sigma^2=4$ , so $\sigma=2$ .

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CBSE 2026Set MARCH1 markMCQ
$Q. In normal distribution, usually which limits include 99% of the observations?$
(a) $\mu \pm 1.96\sigma$
(b) $\mu \pm 2\sigma$
(c) $\mu \pm 3\sigma$
(d) $\mu \pm 2.57\sigma$
›Reveal solutionSolution

About $99\%$ of a normal distribution lies within $\mu\pm2.57\sigma$ (about $2.58\sigma$ ).

Standard normal area results: $\mu\pm1.96\sigma$ covers about $95\%$ , $\mu\pm3\sigma$ covers about $99.73\%$ , and $\mu\pm2.57\sigma$ (more precisely $2.58\sigma$ ) covers about …

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CBSE 2026Set MARCH1 markMCQ
$Q. For a normal distribution, approximate value of mean deviation is 20. Which of the following is the value of quartile deviation?$
(a) $\dfrac{25}{3}$
(b) $\dfrac{32}{3}$
(c) $24$
(d) $\dfrac{50}{3}$
›Reveal solutionSolution

Using $QD:MD:SD=10:12:15$ , $QD=\tfrac{10}{12}(20)=\tfrac{50}{3}$ .

For a normal distribution the approximate relations are $QD\approx\tfrac23\sigma$ and $MD\approx\tfrac45\sigma$ , giving $QD:MD:SD=10:12:15$ . Therefore

$QD=\frac{10}{12}\times MD=\frac{10}{12}\times20=\frac{200}{12}=\frac{50}{3}.$ …

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CBSE 2026Set MARCH1 mark
$Q. What is the shape of normal curve?$
›Reveal solutionSolution

The normal curve is a symmetric, single-peaked, bell-shaped curve.

The graph of the normal distribution is a smooth, bell-shaped curve. It is perfectly symmetric about its mean $\mu$ (where mean $=$ median $=$ mode), rises to a single maximum at $x=\mu$ , and falls off equally on both sides. Its two tails extend to $-\infty$ and $+\infty$ …

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CBSE 2025Set MARCH1 markMCQ
$X = \mu$
(a) $0$
(b) $0.5$
(c) $1$
(d) $-0.5$
›Reveal solutionSolution

The normal curve is symmetric about $X = \mu$ , so the area on either side of the mean is $0.5$ — option (b).

GSEB Class-12 Statistics, Normal Distribution:

…

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CBSE 2025Set MARCH1 markMCQ
$Q. Mean and the first quartile for a normal distribution are 15 and 11 respectively. Which of the following is the value of the third quartile?$
(a) $8$
(b) $14$
(c) $19$
(d) $10$
›Reveal solutionSolution

By the symmetry of the normal curve, $Q_3 = 2\mu - Q_1 = 2(15) - 11 = 19$ — option (c).

GSEB Class-12 Statistics, Normal Distribution:

For a normal distribution the quartiles are placed symmetrically about the mean:

$Q_1 = \mu - 0.6745\,\sigma, \qquad Q_3 = \mu + 0.6745\,\sigma$

…

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CBSE 2025Set MARCH1 mark
$Q. The approximate value of mean deviation for a normal distribution is 12. Find its standard deviation.$
›Reveal solutionSolution

With M.D. $\approx \tfrac{4}{5}\sigma = 12$ , the standard deviation is $\sigma = \tfrac{5}{4}\times 12 = 15$ .

GSEB Class-12 Statistics, Normal Distribution:

A property of the normal distribution is that its mean deviation is approximately:

$\text{M.D.} = \frac{4}{5}\,\sigma$

…

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CBSE 2023Set MARCH1 markMCQ
$X = \mu$
(a) (A) $0$
(b) (B) $-0.5$
(c) (C) $1$
(d) (D) $0.5$
›Reveal solutionSolution

By symmetry of the normal curve about the mean, the area to the left of $X=\mu$ is half of the total, i.e. $0.5$ . Option (D).

The total area under a normal curve equals $1$ . The curve is perfectly symmetric about the mean $\mu$ , so the vertical line at $X=\mu$ divides the total area i …

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CBSE 2023Set MARCH1 markMCQ
$Q. Which of the following is the approximate value of mean deviation for normal variable?$
(a) (A) $\frac{4}{5}\sigma$
(b) (B) $\frac{4}{5}\mu$
(c) (C) $\frac{2}{3}\sigma$
(d) (D) $\frac{2}{3}\mu$
›Reveal solutionSolution

The mean deviation of a normal variable is approximately $\dfrac{4}{5}\sigma$ . Option (A).

Among the standard measures of dispersion for a normal distribution, the mean deviation (about the mean) is a fixed multiple of the standard deviation. Its approximate value is

$\text{M.D.}\approx\frac{4}{5}\sigma\;(=0.8\,\sigma),$ …

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CBSE 2023Set MARCH1 mark
$Q. What is the shape of normal curve?$
›Reveal solutionSolution

The normal curve is a symmetric, bell-shaped, unimodal curve.

The graph of a normal distribution is a smooth, continuous, bell-shaped curve. It is symmetric about its mean $\mu$ , has a single peak (unimodal) at $x=\mu$ , and its two tails extend indefinitely on both sides, …

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CBSE 2022Set MARCH1 markMCQ
$\mu$
(a) 0
(b) 0.5
(c) 1
(d) $-0.5$
›Reveal solutionSolution

Because the normal curve is symmetric about $\mu$ , the area to the left of the perpendicular at $\mu$ is exactly half the total area, i.e. $\mathbf{0.5}$ .

…

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CBSE 2022Set MARCH1 markMCQ
$N(20, 4)$
(a) $(18, 22)$
(b) $(16, 24)$
(c) $(14, 26)$
(d) $(12, 28)$
›Reveal solutionSolution

With $\mu=20$ , $\sigma=\sqrt{4}=2$ , the interval covering $99.73\%$ is $\mu\pm 3\sigma = 20\pm 6 = \mathbf{(14,26)}$ .

Given: $N(20,4)$ means mean $\mu=20$ and variance $\sigma^2=4$ , so $\sigma=2$ .

…

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CBSE 2022Set MARCH1 mark
$\mu - 2\sigma$
›Reveal solutionSolution
The area under the normal curve between $\mu-2\sigma$ and $\mu+2\sigma$ is about $\mathbf{95.45\%}$ .

Explanation (empirical rule). For a normal distribution:

$\mu \pm 1\sigma$ covers about $68.27\%$ ,

$\mu \pm 2\sigma$ covers about $95.45\%$ , …
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Q.If the distribution of normal variable is shown as $N(20, 4)$ then which of the following intervals includes 99.73% of observations?

Concept understanding — Properties of the Normal Distribution

Q.If the distribution of normal variable is shown as N(20,4)N(20, 4)N(20,4) then which of the following intervals includes 99.73% of observations?

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Q.If the distribution of normal variable is shown as $N(20, 4)$ then which of the following intervals includes 99.73% of observations?

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