it is a ppt on statistics

1. PRESTIGE
INSTITUTE OF MANAGEMENT ,
GWALIOR
Submitted by:
RAHUL KAPOLIYA
MBA-1ST C
Submitted to :
PROF. AMRITA SHRIVASTAVA
BINOMIAL DISTRIBUTION

2. Uses of binomial distribution
The binomial distribution can be used when :
 The outcomes or results of each trial in the process are
characterized as one of two types of possible outcomes. In
other words, they are attributes.
 The possibility of outcome of any trial does not change and
is independent of the results of previous trials.

3. Conditions for the applicability of
binomial distribution
For the applicability of binomial distribution in an experiment, the
following conditions must be satisfied :
 The experiment is performed for a finite and fixed number of
trials.
 The trials do not depend on each other.
 Each trial must surely result in either a success or a failure.
 The probability of success in each trial is the same.

4. Obtaining coefficients of the binomial
For obtaining coefficients from the binomial expansion, the following rules may be
remembered.
To find the terms of the expansion of (q+p)
— The first term is qn
— The second term is nC1qn-rp
— In each succeeding term the power of q is reduced by 1 and the power of p is
increased by 1.
— The coefficient of any term is found by multiplying the coefficient of the
preceding term by the power of q in that preceding term, and dividing the
products so obtained by one more than the power of p in that preceding term.
when we expend (q+p) , we get
(q+p)n = qn + nC1qn-1p + nC2qn-2p2 + ………………….. nCrqn-rpr

5. Properties of the binomial
distribution
 The shape and location of binomial distribution changes as p
changes for a given n or as n changes for a given p. As p
increases for a fixed n, the binomial distribution shifts to the
rights.
 The mode of the binomial distribution is equal to the value of x
which has the largest probability.
 As n increases for a fixed p, the binomial distribution moves to
the right and spreads out. The mean of the binomial
distribution, np, obviously increases as n increases with p held
constant.

6. Assumption of binomial distribution
Trials are repeated
All trials should be independent
The number of trial (n) should be fixed
There are two mutually exclusive outcomes in each trial, success and
failure.