This presentation discusses binomial probability distributions through the following key points: - It defines basic terminology related to random experiments, events, and variables. The binomial distribution specifically describes discrete data from Bernoulli processes. - It outlines the notation and assumptions for binomial distributions, including that there are two possible outcomes for each trial (success/failure), a fixed number of trials, and constant probabilities of success/failure. - It presents three methods for calculating binomial probabilities: the binomial probability formula, table method, and using technology like Excel. - It discusses measures of central tendency and dispersion for binomial distributions and how the shape of the distribution depends on the number of trials and probability of success. - Real-world

1. Slide 1Copyright © 2007 Pearson Education, Inc Publishing as Pearson Addison-Wesley.
A
Presentation On
Binomial Probability Distributions
By
Tayab Ali (M/12/ME-11)
ME- Industrial and Production
Jorhat Engineering College

2. Slide 2
Outcome:- The end result of an experiment.
Random experiment:- Experiments whose
outcomes are not predictable.
Random Event:- A random event is an outcome or
set of outcomes of a random experiment that share a
common attribute.
Sample space:- The sample space is an exhaustive
list of all the possible outcomes of an experiment,
which is usually denoted by S.
Basics and terminology

3. Slide 3
Basics and terminology (contd.)
Mutually Exclusive Event.
Random Variables.
 Discrete Random Variable .
 Continuous Random Variable.
Binomial Distribution:-
The Binomial Distribution describes discrete , not
continuous, data, resulting from an experiment
known as Bernoulli process.

4. Slide 4
Notation(parameters) for Binomial
Distributions.
S and F (success and failure) denote two possible
categories of all outcomes.
P(S) = p (p = probability of success)
P(F) = 1 – p = q (q = probability of failure)
n =denotes the number of fixed trials.

5. Slide 5
Notation(parameters) for Binomial
Distributions( contd.)
p =denotes the probability of success in one of the
n trials.
q =denotes the probability of failure in one of the
n trials.
P(x) =denotes the probability of getting exactly x
successes among the n trials.
• x = denotes a specific number of successes in n
trials, so x can be any whole number between 0
and n, inclusive.

6. Slide 6
Assumptions for binomial
distribution
For each trial there are only two possible
outcomes on each trial, S (success) & F (failure).
The number of trials ‘ n’ is finite.
For each trial, the two outcomes are mutually
exclusive .
P(S) = p is constant. P(F) = q = 1-p.
 The trials are independent, the outcome of a
trial is not affected by the outcome of any other
trial.
The probability of success, p, is constant from
trial to trial.

7. Slide 7
Methods for Finding Probabilities
 Method 1: Using the Binomial Probability Formula.

8. Slide 8
Method 1: Using the Binomial
Probability Formula.
For x = 0, 1, 2, . . ., n
Where
n = number of trials.
x = number of successes among n trials.
p = probability of success in any one trial.
q = probability of failure in any one trial.
(q = 1 – p).

9. Slide 9
Method 2: Table Method
Part of A Table is shown below. With n = 12 and p = 0.80
in the binomial distribution, the probabilities of 4, 5, 6,
and 7 successes are 0.001, 0.003, 0.016, and 0.053
respectively.

10. Slide 10
Method 3: Using Technology
STATDISK, Minitab, Excel and the TI-83 Plus
calculator can all be used to find binomial
probabilities.
STATDISK Minitab

11. Slide 11
Excel TI-83 Plus calculator

12. Slide 12
Measures of Central Tendency and dispersion for
the Binomial Distribution.
Mean, µ = n*p
Std. Dev. s =
Variance, s 2 =n*p*q
Where
n = number of fixed trials
p = probability of success in one of the n trials
q = probability of failure in one of the n trials

13. Slide 13
Shape of the Binomial Distribution
The shape of the binomial distribution depends on the values of n
and p.
Fig.1.Binomial distributions for different values of p with n=10
•When p is small (0.2), the binomial distribution is skewed to the
right.
•When p= 0.5 , the binomial distribution is symmetrical.
•When p is larger than 0.5, the distribution is skewed to the left.

14. Slide 14
Fig.2.Binomial distributions for different values of n with p=0.2
Fig. 2 illustrates the general shape of a family of binomial distributions
with a constant p of 0.2 and n’s from 7 to 50. As n increases, the
distributions becomes more symmetric.

15. Slide 15
Applications for binomial distributions
Binomial distributions describe the possible number of times that
a particular event will occur in a sequence of observations.
They are used when we want to know about the occurrence of an
event, not its magnitude.
• In a clinical trial, a patient’s condition may improve or not. We study
the number of patients who improved, not how much better they feel.
•Is a person ambitious or not? The binomial distribution describes the
number of ambitious persons, not how ambitious they are.
•In quality control we assess the number of defective items in a lot of
goods, irrespective of the type of defect.
Examples

16. Slide 16
Areas of Application
• Common uses of binomial distributions in business include quality
control. Industrial engineers are interested in the proportion of
defectives .
• Also used extensively for medical (survive, die)
• It is also used in military applications (hit, miss).

17. Slide 17
Thank You