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Probability and Normal Distribution

PROBABILITY
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Probability and Normal Distribution
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INTRODUCTION TO PROBABILITY
We introduce the idea that research
studies begin with a general question
about an entire population, but actual
research is conducted using a sample
POPULATION
Inferential Statistics
SAMPLE
Probability
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Probability and Normal Distribution
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THE ROLE OF PROBABILITY IN
INFERENTIAL STATISTICS
 Probability is used to predict what kind of
samples are likely to obtained from a
population
 Thus, probability establishes a connection
between samples and populations
 Inferential statistics rely on this connection
when they use sample data as the basis for
making conclusion about population
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Probability and Normal Distribution
PROBABILITY DEFINITION
The probability is defined as a fraction or a
proportion of all the possible outcome
divide by total number of possible outcomes
Probability of A
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=
Number of outcome
classified as A
Total number of
possible outcomes
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Probability and Normal Distribution
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EXAMPLE
 If you are selecting a card from a
complete deck, there is 52 possible
outcomes
• The probability of selecting the king of
heart?
• The probability of selecting an ace?
• The probability of selecting red spade?
 Tossing dice(s), coin(s) etc.
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Probability and Normal Distribution
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PROBABILITY and
THE BINOMIAL DISTRIBUTION
When a variable is measured on a scale
consisting of exactly two categories, the
resulting data are called binomial (two
names), referring to the two categories
on the measurement
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Probability and Normal Distribution
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PROBABILITY and
THE BINOMIAL DISTRIBUTION
 In binomial situations, the researcher
often knows the probabilities associated
with each of the two categories
 With a balanced coin, for example
p (head) = p (tails) = ½
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Probability and Normal Distribution
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PROBABILITY and
THE BINOMIAL DISTRIBUTION
 The question of interest is the number
of times each category occurs in a series
of trials or in a sample individual.
 For example:
• What is the probability of obtaining 15
head in 20 tosses of a balanced coin?
• What is the probability of obtaining more
than 40 introverts in a sampling of 50
college freshmen
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Probability and Normal Distribution
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TOSSING COIN
 Number of heads obtained in 2 tosses a coin
• p = p (heads) = ½
• p = p (tails) = ½
 We are looking at a sample of n = 2 tosses,
and the variable of interest is X = the number
of head
The binomial
distribution showing
the probability for the
number of heads in 2
coin tosses
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1
2
Number of heads in 2 coin tosses
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Probability and Normal Distribution
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TOSSING COIN
Number of heads in 3
coin tosses
Number of heads in 4 coin tosses
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Probability and Normal Distribution
The BINOMIAL EQUATION
(p +
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n
q)
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Probability and Normal Distribution
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LEARNING CHECK
 In an examination of 5 true-false
problems, what is the probability to
answer correct at least 4 items?
 In an examination of 5 multiple choices
problems with 4 options, what is the
probability to answer correct at least 2
items?
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Probability and Normal Distribution
PROBABILITY and NORMAL DISTRIBUTION
σ
μ
In simpler terms, the normal distribution is
symmetrical with a single mode in the
middle. The frequency tapers off as you move
farther from the middle in either direction
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Probability and Normal Distribution
PROBABILITY and NORMAL DISTRIBUTION
μ
X
Proportion below the curve  B, C, and D area
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Probability and Normal Distribution
B and C area
X
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Probability and Normal Distribution
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B and C area
X
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Probability and Normal Distribution
B, C, and D area
μ
X
B+C=1
C+D=½B–D=½
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Probability and Normal Distribution
B, C, and D area
X
μ
B+C=1
C+D=½B–D=½
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Probability and Normal Distribution
The NORMAL DISTRIBUTION following
a z-SCORE transformation
34.13%
13.59%
2.28%
-2z
-1z
0
+1z
+2z
μ
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Probability and Normal Distribution
34.13%
σ=7

13.59%
2.28%
-2z
-1z
0
μ = 166
+1z
+2z
Assume that the population of Indonesian adult
height forms a normal shaped with a mean of μ = 166
cm and σ = 7 cm
• p (X) > 180?
• p (X) < 159?
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Probability and Normal Distribution
34.13%
σ=7
13.59%
2.28%
-2z
-1z
0
μ = 166
+1z
+2z
Assume that the population of Indonesian adult
height forms a normal shaped with a mean of μ = 166
cm and σ = 7 cm
• Separates the highest 10%?
• Separates the extreme 10% in the tail?
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Probability and Normal Distribution
34.13%
σ=7

13.59%
2.28%
-2z
-1z
0
+1z
μ = 166
+2z
Assume that the population of Indonesian adult
height forms a normal shaped with a mean of μ = 166
cm and σ = 7 cm
• p (X) 160 - 170?
• p (X) 170 - 175?
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Probability and Normal Distribution
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EXERCISE
 From Gravetter’s book page 193
number 2, 4, 6, 8, and 10
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