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Stat 201 Handout  updated version
(June 4, 2003)
More on Coin Tossing and the Normal distribution
Review: Examples from class
1. Toss coin 5 times. Random variable of interest is
X=# heads
.
{
Computed and graphically displayed probability distribution for
X
.
{
Demonstrated idea of
P(X=x)
being equal to the area
associated with
x
under the
probability
distribution histogram
.
{
Introduced idea of discrete
r.v.'s and continuous
r.v.'s.
2. Randomly guess answers on exam. R.v. of interest is
X=exam mark out of 100
. Know
X
has normal
distribution with mean 21.7 and SD 8.49.
{
Discussed
P(X=50)=0
. (Similarly for
P(X=x)
for any single value of
x
.)
{
Computed
P(pass)=P(X >= 50)
:
±
Need to standardize
X
(change scale to
Z
scale):
////////////>
x
21.7
30.19
50
////////////>
z
0
1
5021.7

8.49
P(X>=50)=P
( (X21.7)/8.49 >= (5021.7)/8.49 ) = P(Z
>=3.33)
z
Use normal table on pp. 538539 to find areas under the normal curve:
{
areas listed are left tails  correspond to
P(Z<=z)
for given values of
z
z
Read off
P(Z<=3.33)=P(Z<3.33)=0.9996
. So
P(X>=50)=P(Z>=3.33)=1P
(Z<3.33)=10.9996=0.0004
.
Binomial Distribution
For
Example 1
above, we have a special name for the distribution of
X
. We say "
X has a binomial distribution
with n=5 and p=0.5
." We write
X~Bin(n=5,p=0.5)
.
Definition
A binomial distribution results from a random operation involving
n
independent success

failure
trials
with a common probability of success
p
. The total number of successes has a
Bin(n,p)
Page 1 of 4
3/26/2011
http://www.stat.sfu.ca/~sgchiu/Grace/S201/Handouts/h3.html
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More examples of binomial r.v.'s
a. For any given beefcow, there is a 0.2 probability for it to have BSE (mad cow disease). Your herd has 38
animals.
X
is the total number of cows in your herd that have BSE. So
X~Bin(n=38,p=0.2)
.
b. From
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This note was uploaded on 01/23/2012 for the course STAT 201 taught by Professor Staff during the Fall '03 term at Simon Fraser.
 Fall '03
 STaff
 Normal Distribution, Probability

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