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NORMAL DISTRIBUTION — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsNORMAL DISTRIBUTION3 Marks
Question
State the properties of standard normal distribution.
✓

Answer

Some important properties of standard normal distribution are as follows :
$(1)$ It is a distribution of continuous random variable.
$(2)$ The curve of this distribution is completely bell-shaped.
$(3)$ The tails of the curve of this distribution are asymptotic to $X$-axis, i.e., they never touch $X$-axis.
$(4)$ The mean of this distribution is $0 ($zero$)$ and its variance and standard deviation is $1 .$
$(5)$ In this distribution the values of mean, median and mode are zero.
$(6)$ In this distribution the estimated values of $Q_{1}$ and $Q_{3}$ are as under: $Q_{1} \approx-0.675, Q_{3} \approx 0.675$
$(7)$ The curve of this distribution is completely symmetric about $Z=0$ and its skewness is zero.
$(8)$ The area of the curve of this distribution bounded by $X$-axls and on both sides of $Z=0$ is equal to $0.5 .$
$(9)$ In this distribution, $(i)$ Quartile deviation $\approx \frac{2}{3}$ $(ii)$ Mean deviation $\approx \frac{4}{5}$
$(10)$ The important areas related to standard normal curve are as follows: $(i)$ The area under the curve between $z=\pm 1$ is $0.6826$ $(ii)$ The area under the curve between $z=\pm 2$ is $0.9545$ $(iii)$ The area under the curve between $z=\pm 3$ $(iv)$ The area under the curve between $z=\pm 1.96$ is $0.95$ $(v)$ The area under the curve between $z=\pm 2.575$ is $0.99$

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