this ppt for making decision regarding risk in business.

2. Types of Distribution
 Frequency Distribution
 Normal (Gaussian) Distribution
 Probability Distribution
 Poisson Distribution
 Binomial Distribution
 Sampling Distribution
 t distribution
 F distribution

3. Introduction
Introduce
1734
 De Moivre 1667-1754
Modify
1809
 Gauss 1777-1855

4. What is Normal (Gaussian)
Distribution?
Normal distribution
Pattern
Set of data
Bell shaped curve
(Friedrich Gauss)

5. Characteristics of Normal
Distribution
1) All normal curves are bell-shaped.
2) All normal curves are symmetric about the mean
μ.
3) The area under an entire normal curve is 1.
4) The height of any normal curve is maximized at
x = µ.
5) The shape of any normal curve depends on its
mean μ and standard deviation σ.
6) Above mean are + and below mean are - .

7. Advantages of Normal
distribution
 Tractable and analytically
 Symmetry
 Large variety of distributions in large samples.

8. Basics of normal
distribution
 Bell Curve
 Area under entire curve = 1 or 100%
 Mean = Median
 This means the curve is symmetric

9.  Two parameters
 Mean μ (pronounced “meeoo”)
 Locates center of curve
 Splits curve in half
 Shifts curve along x-axis
 Standard deviation σ (pronounced “sigma”)
 Controls spread of curve
 Smaller σ makes graph tall and skinny
 Larger σ makes graph flat and wide
 Ruler of distribution
 Write as N(μ,σ)

10.  Puts all normal distributions on same scale
Any point on normal curve(given)
Mean
Z = Y - µ
σ
SD
how many SD away from the mean

11. Calculate Z score
µ = 70, σ = 3 and Standardize y = 68.
Z = y - µ
σ
= 68 – 70
3
= -0.67
y = 68 is 0.67 standard deviations below the mean

12. Solving Problems
 The demand of
product is known to
be normally
distributed with mean
70 and standard
deviation 3.
 Y(mean)~ N(SD)-
 (70-mean,3-SD)

13. Solving Problems
 What percent of products are
lesser than 66 (demand) ?
 P-%(Y-point on curve (men)
< 66)
= P(Z<66 –70)
3
=P(Z<-1.33(table)
=1-0.9082(1.33table)
= 0.0918

15. Solving Problems
• What percent of products
are lesser than 74
(demand)?
• (Y P> 74) = 1-P(Y-men<74)
= 1 – P(Z< 74 – 70 )
3
= 1 – P(Z<1.33)
= 1 – 0.9082(1.33table)

16. Solving Problems
• What percent of products are
between 68 and 71 (demand)?
• P(68 < Y < 71)
= P(Y<71) – P(Y<68)
=P(Z< 71-70 )-P(Z< 68-70 ) )
3 3
=P(Z<0.33) - P(Z<-0.67)
= 0.6293(0.33table) –
1 - 0.2514(0.67table)
= 0.3779