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| PROBLEM
1: DISCRETE DISTRIBUTIONS |
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| 5.55 |
Only 1% of all American
households have only |
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a black and white
television set. A television |
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marketing analyst
randomly selects 160 American |
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households. |
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a. How many households would he expect to
have |
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only a black-and-white
television set? |
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b. What is the probability that eight or more |
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households have only a
black-and-white |
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television set? |
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c. What is the probability that between two
and |
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six households
(inclusive) have only a black-and- |
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white television set? |
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| SOLUTION: |
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a. How many households would he expect to
have |
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only a black-and-white
television set? |
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n= |
160 |
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p= |
0.01 |
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m = |
n.p |
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m = |
160 (.01) |
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m = |
1.6 |
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b. What is the probability that eight or more |
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households have only a
black-and-white |
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television set? |
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n= |
160 |
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q = |
1-p |
or |
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p= |
0.01 |
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p(8) = |
nCx.px.qn-x= |
n! |
.px.qn-x |
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p(8) = |
160C8.(.01)8.(.99)152 |
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p(8) = |
0.0004 |
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c. What is the probability that between two
and |
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six households
(inclusive) have only a black-and- |
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white television set? |
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p(2) = |
160C2.(.01)2.(.99)158 |
= |
0.2598 |
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p(3) = |
160C3.(.01)3.(.99)157 |
= |
0.1381 |
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p(4) = |
160C4.(.01)4.(.99)156 |
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0.0540 |
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p(5) = |
160C5.(.01)5.(.99)155 |
= |
0.0172 |
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p(6) = |
160C6.(.01)6.(.99)154 |
= |
0.0045 |
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P (2) & P (6) |
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0.4736 |
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