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Normal
Distribution –Find The
Value of μ & σ
SUNDARA B. N.
Assistant
Professor
Problem
In a normal
distribution 10% of
the items are over
125 and 35% are
under 60. Find the
mean and Standard
Deviation ...
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<...
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....
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
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
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Normal Distribution - Find the Value of Mue and Standard Deviation

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

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Normal Distribution - Find the Value of Mue and Standard Deviation

  1. 1. Normal Distribution –Find The Value of μ & σ SUNDARA B. N. Assistant Professor
  2. 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. 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. 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. 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. 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

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