Question
Define normal distribution and state the characteristics of normal curve.
✓
Answer
The distribution of a normal variable $X$ is called Normal distribution. It is denoted by $N\left(\mu, \sigma^{2}\right)$ The characteristics of normal curve:
$(1)$ It is completely bell-shaped.
$(2)$ It is asymptotic to $X$-axis, I.e., the tails of the curve never touch $X$-axis.
$(3)$ The total area of the region bounded by normal curve and $X$-axis $=$ Total probability $1$
$(4)$ It is symmetric about the sides of meai p of normal variate. So the area of the regiol of normal curve on both the sides of $X=\mu$ is equal to $0.5$.
$(5)\ P[\mu \leq X \leq a]$ is the area of region bounde by $X$-axis and two perpendicular lines at $X=$ and $X=a$.
$(6)$ To find the area under the normal curve the normal variable is transformed to standan normal variable $Z$ and readymade table is used.
$(1)$ It is completely bell-shaped.
$(2)$ It is asymptotic to $X$-axis, I.e., the tails of the curve never touch $X$-axis.
$(3)$ The total area of the region bounded by normal curve and $X$-axis $=$ Total probability $1$
$(4)$ It is symmetric about the sides of meai p of normal variate. So the area of the regiol of normal curve on both the sides of $X=\mu$ is equal to $0.5$.
$(5)\ P[\mu \leq X \leq a]$ is the area of region bounde by $X$-axis and two perpendicular lines at $X=$ and $X=a$.
$(6)$ To find the area under the normal curve the normal variable is transformed to standan normal variable $Z$ and readymade table is used.
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