Question

Which of the following are correct regarding normal distribution curve?
(i) Symmetrical about the line $X=\mu$ (Mean)
(ii) Mean $=$ Median $=$ Mode
(iii) Unimodal
(iv) Points of inflexion are at $X=\mu \pm \sigma$

• A. (i), (ii)
• B. (ii), (iv)
• C. (i), (ii), (iii)
• D. All of these

Answer 1

Answer: (D)

All of these

In a normal distribution , mean, median and mode are equal. The curve is bell type curve which is symmetric about

$x=$ mean (mode or median).
It is unimodal as it has its first derivative $0$ at $x=\mu$ (mean) and the derivative is less than $0$, for $x>\mu$ and greater than $0$ for $x<\mu$
It has its point of inflection (second derivative $0$) at $x=\mu +\sigma$ and $x=\mu -\sigma$ where $\sigma$ is the standard deviation.