State the properties of normal distribution.

Question

Accepted Answer

1. It is a distribution of continuous random variable
2. Parameters are $\mu$ (mean) and $\sigma$ (standard deviation)
3. Distribution is symmetric about $\mu$, skewness is zero
4. Mean = Median = Mode, i.e. $\mu = M = M_0$
5. Quartiles are equidistant from median: $Q_3 - M = M - Q_1$
6. The probability curve is completely bell shaped
7. Normal curve is asymptotic to X-axis (tails never touch X-axis)
8. $Q_1 = \mu - 0.675\sigma$ and $Q_3 = \mu + 0.675\sigma$
9. Quartile deviation $= \frac{2}{3}\sigma$ (approximately)
10. Mean deviation $= \frac{4}{5}\sigma$ (approximately)
11. Total area under normal curve is 1