#### Chapter 9 - Binomial Distribution

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Transcript Chapter 9 - Binomial Distribution

Chapter 9
Binomial Distribution
James A. Van Slyke
Azusa Pacific University
Binomial Distribution
5 Conditions that need to be met:
1.
There is a series of N trials
2. For each trial there are only two possible
outcomes
3. For each trial, the two outcomes are
mutually exclusive
Binomial Distribution
5 Conditions that need to be met:
4.
Independence between the outcomes of
each trial
5. The probability for each outcome, stays the
same from trial to trial
Informs us of the probability of getting an
outcome based on N
Example: Flipping a Coin
Each flip is a particular trial
Only 2 possible outcomes
Mutually exclusive – only a head or tail
can occur
Independent – outcome of one flip doesn’t
affect any other flips
Example: Flipping a Coin
number of outcomes classifiable as heads
p(head) = p(H) =
Total number of outcomes
1
= 0.5000
2
Number of outcomes classifiable as tails
p(tail) = p(T) =
Total Number of outcomes
1
= 0.5000
2
Binomial Expansion
Equation for basic aspects of probability
Each letter represents an event
Each exponent tells the number of that kind of
event
P Q
N
P = probability of first possible outcome
Q = probability of second possible outcome
N = number of trials
Binomial Distribution
The distribution may be given for any N, P
and Q
The distribution is symmetrical
As N increases, the distribution
approximates a normal curve
Binomial Table
Table shows the results for the binomial
expansion
Solved
for various values of N, P, and Q
Solved for various numbers of P or Q events
The table can be used with P or Q
Homework
2, 3, 4, 5, 8, 9, 16