This ppt explains how to find the value of Mue and Standard Deviation in Normal Distribution which will helpful in Solving problems

1. Normal
Distribution –Find The
Value of μ & σ
SUNDARA B. N.
Assistant
Professor

2. Problem
In a normal
distribution 10% of
the items are over
125 and 35% are
under 60. Find the
mean and Standard
Deviation of the
distribution.
35% 10%
X=60
Z=-z₁
μ
Z₂
X=12
5
0

3. Given Information
Let X~N(μ, σ²), where μ, σ² are unknown and are
to be obtained.
Here we are given
P(X>125) =0.1 and P(X<60) =0.35
We know that if X~N(μ, σ²), then the S.N.V is
given by
Z = X – μ
σ

4. Equations
Now P(X<60)=P(Z<-z₁)=0.35
= P(Z>z₁)=0.35
= 0.5-P(0<Z<z₁)=0.35
= P(0<Z<z₁)=0.15
= z₁=0.39
and P(X>125)=P(Z>z₂)=0.10
=0.5-P(0<Z<z₂)=0.10
=P(0<Z<z₂)=0.40
z₂=1.28
= -z₁(say)….(1)
=
z₂(say)….(2)

5. Putting the values of z₁ and z₂ in Equation 1 and 2
= -0.39
= 1.28
……(3)
……(4)
= 1.28+0.39
= 1.67
= 38.92

6. Value of μ and σ
From Eq. (4),
μ=125-1.28σ
μ=125-1.28x38.92
=75.18
Hence μ=mean=75.18;
σ=SD=38.92