• The field of statistics deals with the
collection, presentation, make
decisions, solve problems, and design
• Engineering statistics combines
engineering and statistics
• Statistical approaches can provide the
basis for making decisions.
• Reliability engineering use statistics.
• Quality control and process control use
• Time and methods engineering use
The probability that the variable takes a value less than or equal to specified x.
Arrangement of values of a variable showing their observed or theoretical
frequency of occurrence
The distribution is of discrete and continuous variable.
Description of the relative numbers of times each possible outcome will
It is non decreasing.
It is non negative.
Distributions have different shapes.
• Statistical distribution is used in many field of real life.
• An engineer must determine the strength of supports for
generators at a power plant. A number of those available must
be loaded to failure and their strengths will provide the basis for
assessing the strength of other supports.
• Groups of networked computers which have same goal for
• Bits are sent over a communications channel in packets of 12. If
• the probability of a bit being corrupted over this channel is 0.1
and such errors are independent, what is the probability that no
more than 2 bits in a packet are corrupted?
• Used in processing language to assign distribution.
• Many probability distributions are so
important in theory or applications that they
have been given specific names.
• The main types of distribution are as follows.
Hyper geometric distribution
Negative binomial distribution
• The types are related to each other in some
• Swiss mathematician Jakob Bernoulli, in a proof
published posthumously in 1713, determined
that the probability .Hence the name binomial
• In 1936 the British statistician Ronald Fisher
used the binomial distribution to publish
evidence of possible scientific theory.
• The work of jakob was published in ARTS
CONJECTANDI IN BASEL IN 1713.
• The binomial distribution is the discrete
probability distribution of the number of
successes in a sequence of n independent each
of which yields success with probability p
• To model the number of successes in a sample of size n drawn
with replacement from a population of size N.
• Without replacement, it is called as the hyper geometric
• The parameters are n,p and denoted by (x;n,p).
• The important points for this are as follows:
Two out comes: success and failure
The successive trails are independent.
The probability of success remain constant
The experiment is repeated at fixed no of times.
• Binomial distribution occurs whenever
there is a success and fail.
• The outcome may be trail or head, success
and failure, wrong and right,
• Some general examples are:
A fair coin is tossed five times.
probability of obtaining the head?
A baseball player comes to bat 4 times in
a game. The chance of a strike-out for this
player is 30%.
• A motor Machine produces 20% defective components. In a
random sample of 6 components. Determine the probability
that: There will be 3 defective components
• The output of an automated machine is inspected by taking
samples of 6 items. If the probability of a defective item is
0.25, find the probability of having ,two defective items.
• The probability of obtaining a defective resistor is given by
1/10 .In a random sample of 9 resistors, what is the probability
of 3 defective resistors.
• The probability of successful transmission of signal to receiver
is 0.25. if there are 6 signals what is the probability of
successful reception of 3 signals
• If a new drug is introduced to cure a disease
then it either cure the disease or doesn’t.
• If a person purchase a lottery ticket then he is
either going to win it or not.
• the number of successful sale calls.
• The no of defective products in a production
• The experience of a house agent indicated
that he can provide suitable accommodation
for 75 percent clients. if 6 clients approach to
him then what is the probability for 4 clients?
• A binomial experiment (also known as a
Bernoulli trial) is a statistical experiment that
has the following properties:
The experiment consists of n repeated trials.
Each trial can result in just two possible
outcomes. We call one of these outcomes a
success and the other, a failure.
The probability of success, denoted by P, is
the same on every trial.
The trials are independent; that is, the
outcome on one trial does not affect the
outcome on other trials.
Hyper geometric is the distribution like binomial one but with replacement of
If N is large then it becomes binomial distribution.
The Poisson distribution is for rare events .the Poisson distribution cases
can be handled with binomial one.
The negative distribution is when the trials are variables to reach the fixed
The geometric distribution is the one in which the trials are variable
to reach the first success.
The geometric distribution is the special case of negative distribution
Statistics play a very important role in engineering. This
is because most engineering projects have to be
precisely calculated with every little detail recorded in
order for it to work and fit together correctly