The normal distribution curve is symmetrical about
[\(\mu\) = mean, \(\sigma\)= standard deviation]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(x = \mu\)
The normal probability density function is
\( \displaystyle f(x) = \frac{1}{\sigma\sqrt{2\pi}}\, e^{-\frac{(x-\mu)^2}{2\sigma^2}} \)
It depends on x only through \((x - \mu)^2\), so it takes the same value at \(\mu + h\) and \(\mu - h\). The curve is therefore symmetrical about the mean, the line \(x = \mu\), where it has its peak (mean = median = mode).
CBSE Applied Mathematics (Class XII):
Normal Distribution
