3. ™When the data values are evenly
distributed about the mean, a
distribution is said to be a
Normal Distribution (symmetric
distribution).
™A normal distribution is a
continuous, symmetric, bell-
shaped distribution of a variable.
3
NORMAL DISTRIBUTION
4. 4
NORMAL DISTRIBUTION
™The area under a normal distribution
curve is used more often than the values
on the y axis. Therefore, when a normal
distribution is pictured, the y axis is
sometimes omitted
5. ™The mathematical equation for a
normal distribution is;
™Where
ƒ e = 2.718
ƒ = 3.14
ƒ µ = Population Mean
ƒ =Standard Deviation
5
NORMAL DISTRIBUTION
FORMULA
6. ™The shape and position of a
normal distribution curve
depend on two parameters;
ƒ Mean
ƒ Standard Deviation
6
NORMAL DISTRIBUTION
FORMULA
7. ™The curve is continuous.
™The curve is bell-shaped.
™The curve is symmetrical about
the mean.
™The mean, median and mode
are located at the center of the
distribution and are equal to
each other.
7
NORMAL DISTRIBUTION
IMPORTANT PROPERTIES
8. ™The curve never touches the x-
axis
™The total area under the normal
curve is equal to 1.
8
NORMAL DISTRIBUTION
IMPORTANT PROPERTIES
9. ™SEI Auditors have performed the
Class C appraisal of ‘Welcome
Technologies’ for CMMI Level 2,
3, 4 and 5 processes. They
found several NCs in 18 different
process areas. No. of NCs found
in 18 process areas are enlisted
below;
™3, 5, 3, 6, 4, 8, 10, 2, 6, 5, 7, 4,
9, 5, 6, 6, 8, 7
9
NORMAL DISTRIBUTION
CASE STUDY (NCs FROM CMMI PROCESS AUDIT)
10. ™Draw the Frequency Distribution
(Histogram) of given Data
™Analyze the Distribution Curve
10
NORMAL DISTRIBUTION
CASE STUDY (NCs FROM CMMI PROCESS AUDIT)
11. ™Draw the Frequency Distribution Table
11
NORMAL DISTRIBUTION
CASE STUDY (NCs FROM CMMI PROCESS AUDIT)
Classes X Frequency F(x)
2 1
3 2
4 2
5 3
6 4
7 2
8 2
9 1
10 1
19. ™Empirical Rule: (Also called 68-95-
99.7 rule or three sigma rule)
ƒ About 68.27% of the values lie within 1
standard deviation of the mean
ƒ About 95.45% of the values lie within 2
standard deviations of the mean
ƒ About 99.73% of the values lie within 3
standard deviation of the mean
19
NORMAL DISTRIBUTION
AREAS UNDER NORMAL DISTRIBUTION CURVE