Algebra

Probability

Easy

applied

The normal distribution curve is symmetrical about

[ $\mu$ = mean, $\sigma$ = standard deviation]

$x = \sqrt{\mu}$

$x = \mu$

$x = \sigma$

$x = \frac{\mu}{\sigma}$

✅ Correct Option: 2

The normal distribution curve is a bell-shaped curve that has one peak in the middle and slopes down equally on both sides.

When a curve is symmetrical about a vertical line $x = k$ , it means the curve looks exactly the same on both sides of that line, like a mirror image.

For the normal distribution, the line of symmetry passes through the highest point (peak) of the bell curve.

This peak occurs at $x = \mu$ , where $\mu$ is the mean.

The mean represents the center of the distribution, with half the area under the curve on the left of $\mu$ and half on the right of $\mu$ .

The other options do not represent the line of symmetry:

$x = \sqrt{\mu}$ is an arbitrary calculation unrelated to the center of the distribution.

$x = \sigma$ represents the standard deviation, which measures the spread of the curve, not its center.

$x = \frac{\mu}{\sigma}$ is another arbitrary value with no connection to symmetry.

The normal distribution curve is symmetrical about $x = \mu$ .

Therefore, the answer is Option 2: $x = \mu$

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The random variable X has the following probability distribution

X	0	1	2	3
P(X)	a	a	b	b

such that E(x²) = 2E(x), then the value of b is:

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$P(X=x) = \begin{cases} 5k, & x=0 \\ 2k, & x=1 \\ 3k, & x=2 \\ 0, & \text{otherwise.} \end{cases}$

Then, the value of $E(X)$ is :

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If three balls are drawn one by one without replacement from a bag containing 5 white and 4 red balls, then the probability distribution of the number of white balls drawn is

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Probabilities of solving a specific mathematical problem independently by three students are $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$ . If all the three students try to solve the problem independently, the probability that the problem is solved, is:

The normal distribution curve is symmetrical about [μ\muμ = mean, σ\sigmaσ= standard deviation]

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The normal distribution curve is symmetrical about

[ $\mu$ = mean, $\sigma$ = standard deviation]