Properties of Normal Distribution

a.It is a continuous  probability  distribution having  parameters m and .

b.The normal  curve is perfectly symmetrical about  the mean (m) and is  bell shaped. It means that if  we fold  the curve  along  the vertica line  at the  centre the two halves of the  curve  would  coincide. The  two tails of the curve  on either side of x =  m extends to infinity.

c.Mean = Median = Mode skewness = 0.

d.It has only  one mode.

e.Q1 and Q3 are equidistant from  median or mean.

Q1 = m  - 0.67 Q3 = m +0.67 (app)

Quartile Deviation = 0.67 mean deviation  (about  mean) = 0.80= 4/ 5.

f.The maximum  ordinate  is at x= m  its vlaues1/ √2λ.

g.The area  under  the curve  means the area  lying between  the curve  and the  horizontal  axis  and is  equal to  the number  of frequencies. The s distributes this  area  as follows.