Download Normal Distribution

Probability
Prof.Dr.Ramez bedwani
Outcome
• What is meant by a normal distribution & its
uses
Probability
The probability of the occurrence of a
particular event equals the proportion of
times that the event does occur in a large
number of similar repeated trials
Magnitude of probability
• It represents one’s degree of belief in the
occurrence of an event
• In statistics the investigator assigns a prior
probability to the event
(Hypothesis)
study
posterior
probability (probability modified in the light
of the results obtained )
Probability Calculations
Multiplicative rule
• Prob(A and B) = prob (A)x prob(B)
with the condition that A and B are
independent (Conditional probability)
e.g. the sexes of children are independent events
as the probability that the next child is a girl is
not affected by the sexes of the previous
children
Probability Calculations
Additive rule
• Prob (A or B) = prob (A)+ prob (B)– prob (both A,B)
e .g. In Abis area the prob . Of Schisto infection is 70%
(0.7) and of Asceris 40%(0.4) ,whet is the probability Of
having either Schisto OR Ascaris .
• Prob (Schist or Ascaris)=0.7+0.4 – (0.7x0.4)= 1.1 - 0.28 = 0.82
• Provided that : the two events are independent
» When the two events are mutually exclusive
(can not occur together ) A X B = 0
Normal Distribution
Characteristics of
normal distribution
• Symmetric, bell-shaped curve.
• Shape of curve depends on population mean
 and standard deviation .
• Center of distribution is .
• Spread is determined by .
• Most values fall around the mean, but some
values are smaller and some are larger.
Characteristics of Normal Distribution
• It is Symmetric around the mean:
Two halves of the curve are the same (mirror
images)
Examples of normal
random variables
• Blood Pressure level
Definitions
• Mean is located in center, or mode of normal
curve
• The standard deviation is the distance from
the mean to the inflection point of the normal
curve
• the inflection point is the place where the
curve changes from concave down to concave
up.
Construction
• A normal curve is drawn by first drawing a
Histogram and fitting the normal curve
• Next, place the mean, mu on the curve.
• Then place sigma on curve by placing the
segment from the mean to the upper (or
lower) inflection point on your curve.
• From this information, the scale on the
horizontal axis can be placed on the graph
Example
• For any normal curve with
mean mu and standard
deviation sigma:
• 68 percent of the
observations fall within one
standard deviation sigma of
the mean.
• 95 percent of observation
fall within 2 standard
deviations.
• 99.7 percent of
observations fall within 3
standard deviations of the
mean.
Questions
• Draw normal curve with mean=mu=100, and
standard deviation = sigma = 10.
• Draw normal curve with mean = 20, sigma=2.
‫‪Assignment‬‬
‫‪Topic‬‬
‫‪Uses of t-test of significance‬‬
‫‪Students Names‬‬
‫باخوم سدراك نظير سدراك‬
‫باسم خالد محمد‬
‫بسمه مهدي رياض‬
‫بسنت اشرف محمد‬
‫بسنت حسن علي‬
‫تغريد محمود ابراهيم‬
‫حسام الدين حسين محمد‬
‫حسام حسين منصور‬
‫حماده محمد عشري‬
‫حميد عبد االله‬
‫دعاء السيد رشاد‬