Exam 2 Study Guide
B
Y
S
AMANTHA
R
UDA
P
ROBABILITY
D
ISTRIBUTIONS
(C
HAPTER
5)
T
OPIC
7 B
INOMIAL
D
ISTRIBUTION
•
Conditions of a binomial distribution
–
o
success = event occurs, failure = event doesn’t occur
o
Repetitions of a random experiment under identical conditions
are called trials
o
The random variable of interest is X=number of successes in n
trials
o
The probability of success is the same for every trial
denoted
by
π
o
The probability of failure is denoted by 1x
o
Summary
: The experiment consists of n identical trials, the outcome of each trial
is either a success of a failure, the n trials are statistically independent of each
other, with the probability of success
π
remaining the same from trial to trial, x
represents the number of successes.
•
Expected Value
 n
π
•
Variance
 n
π
(1
π
)
•
Standard Deviation

√
n
π
(1
π
)
•
Use factorial formula is trying to find out the probability of getting a
particular outcome (Ex: p(x=2))
•
Parameters of Binomial Distribution:
π
and n
T
OPIC
8 N
ORMAL
D
ISTRIBUTION
•
Normal distribution:
o
Characteristics: bell shaped, unimodal symmetric, mean median and mode lie at
center, parameters are
µ
and
σ,
tails extend indefinitely and never
touch the axis
•
Standard Normal Distribution
o
Mean=0, Standard Deviation = 1
o
Used to find probabilities for any normal distribution
o
Zdistribution since probabilities are derived from standardized z
values
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Population not sampling distribution
o
Standard Normal Zvalues
Z=(x
µ)/ σ
o
To find
probabilities
,
proportions
, or
percentages
for normal curve:
convert x to z, find z in the table, look in the body for the
appropriate probability
•
Calculating Percentiles:
since percentiles are values you use the reverse
process; look up the given probability in the body of the ztable, read
off the appropriate zvalue, using the zvalue solve for x using the
formula Z=(x
µ)/ σ
T
OPIC
9 S
AMPLING
D
ISTRIBUTION
F
OR
T
HE
S
AMPLING
M
EAN
x̄
•
Parameters

number that summarized some aspect of a population or
process, descriptive measure of a population
o
Binomial distribution parameters – n and
π
o
Normal distribution parameters 
µ and σ
•
Estimators
– used when we don’t know parameter values
sample
statistics such as s, x̄, and p
•
Estimators vs. estimates
:
Estimator – a sample statistic use to estimate a population
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 Spring '08
 KUMARSANJAY
 Statistics, Normal Distribution, Standard Deviation, Null hypothesis

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