This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up**This preview shows
pages
1–2. Sign up
to
view the full content.*

Normal Approximation to the Binomial Distribution
Using the Central Limit Theorem
Assume that I select a random sample of size n from a population, where n is “large.”
For each
member of the sample, I want the answer to a yes-or-no question.
For sample member i, let
1
=
i
X
, if the person says, “Yes,” or
0
=
i
X
, if the person says, “No.”
Assume that the fraction
of members of the population who would give “Yes” answers is p.
i)
There is a fixed number, n, of trials.
ii)
The trials are identical to each other, since each one consists of randomly selecting a
member of the population and asking the yes-or-no question.
iii)
The trials are independent of each other, due to random sampling.
iv)
Each trial has two possible outcomes:
Success = {person says, “Yes”} or Failure =
{person says, “No”}.
v)
P(Success) = p for each trial, due to random sampling.
Let
∑
=
=
n
i
i
X
Y
1
.
Then Y ~ Binomial( n, p).
The mean of this distribution is
np
=
μ
, and the
standard deviation is

This
** preview**
has intentionally

This is the end of the preview. Sign up
to
access the rest of the document.

Ask a homework question
- tutors are online