STAT 400
Examples for 09/08/2011
Fall 2011
Binomial Distribution
:
1.
The number of trials,
n
, is fixed.
2.
Each trial has two possible outcomes:
“success”
and
“failure”.
3.
The probability of “success”,
p
, is the same from trial to trial.
4.
The trials are independent.
5.
X
= number of "successes" in
n
independent trials.
Then
(
)
(
)
k
n
k
k
n
k
p
p
k
C
n
p
p
k
n
k


⋅
⋅
=


⋅
⋅
=
=
1
1
P
)
(
X
,
where
k
= 0, 1, … ,
n
.
E
(
X
) =
n
⋅
p
Var
(
X
) =
n
⋅
p
⋅
(
1
–
p
)
SD
(
X
) =
(
)
p
p
n

⋅
⋅
1
1.
Bart Simpson takes a multiple choice exam in his Statistics 101 class.
The exam has
15 questions, each has 5 possible answers, only one of which is correct.
Bart did not
study for the exam, so he guesses independently on every question.
Let
X
denote the
number of questions that Bart gets right.
a)
Is it appropriate to use Binomial model for this problem?
b)
What is the expected number of questions that Bart would get right?
c)
What is the probability that Bart answers exactly 3 questions correctly?
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d)
What is the probability that Bart would get at most 5 of the questions right?
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 Fall '08
 Kim
 Statistics, Binomial, Poisson Distribution, Probability, Probability theory, Binomial distribution, Bart Simpson, Discrete probability distribution, Negative binomial distribution

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