STAT 400
Examples for 09/13/2011
(1)
Fall 2011
5.
Suppose that on Halloween 6 children come to a house to get treats.
A bag
contains 8 plain chocolate bars and 7 nut bars.
Each child reaches into the bag
and randomly selects 1 candy bar.
Let X denote the number of nut bars selected.
a)
Is the Binomial model appropriate for this problem?
No
.
Without replacement
⇒
Trials are not independent.
b)
Find the probability that exactly 2 nut bars were selected.
15
005
5
70
21
6
15
4
8
2
7
,
C
C
C
⋅
⋅
=
≈
0.2937
.
barb2sw
barb2se
7
8
nut
plain
barb2down
barb2down
2
4
OR
⋅
⋅
⋅
⋅
⋅
⋅
10
5
11
6
12
7
13
8
14
6
15
7
2
6
C
≈
0.2937
.
Hypergeometric Distribution
:
N
= population size,
S
= number of “successes” in the population,
N
–
S
= number of “failures” in the population,
n
= sample size.
X
= number of "successes" in the sample when sampling is done without replacement.
Then
n
x
n
x
N
S
N
S
X
C
C
C
N
S
N
S
n
x
n
x
x


⋅
=


⋅
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 Fall '08
 Kim
 Statistics, Probability, Binomial distribution, 10%, 15%, 20%, candy bar, nut bars

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