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Review of Chapter 4
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1. A manufacturer makes light bulbs and claims that their reliability is~ercent.
Reliability is defined to
be the proportion of non-defective items that are produced over the long run. If the company's claim is
.....-COIT\ct,
what is the eXECctednumber of non-defective light bulbs in a random sample of 1,000 bulbs?
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e 0 owmglat bl e lves th epro bability distribution of causes of death in the US.
2 Thfill
Probability
Causes
Cardiovascular disease
0.47
Malignancies
0.22
Accidents
?
Chronic pulmonarv disease 0.04
Pneumonia & influenza
0.03
Diabetes mellitus
0.02
0.01
Suicide
0.16
All other causes
~
What must be the probability that a randomly chosen death was due to an accident in order for this to be a
legitimate probability distribution?
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3. A basketball player's shooting percentage is 55%. He/she attempts ~ts
a) What is the mean number of made shots?
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b) What is the standard deviation?
during the game.
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4. A study of health care recorded the number of visits X to a physician made by a person in a year. Here
is the probability distribution of the random variable X.
''--..0 Visits
0
0.10
Probability
I
0.08
2
0.06
3
0.08
4
0.12
6
0.12
7
0.10
8
0.09
9
0.06
10
0.03
II
0.02
\
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a) What is the mean number ofphysipian visits made by a person in a year')
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b) Whatjs the probability that a person visits a physician less than 3 timys? -.::-
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5. Circle the correct answer.
a) Averages are more"lless ariable than individual observations.
rb) Averages aremo
/less normal than individual observations.
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The distribution of grades (A = 4, B = 3, C = 2, and so on) in a large course is as follows:
o
Outcome
Probability
'0.10
I
0.15
2
0.30
a) Find the mean grade in this course
(
4
3
0.30
0.10)
0.15
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b) Is the mean higher or lower than a B?
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c) Find the ~tandard devil!tion of the grades.
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6. Sixty-Ihe..percent of all divorce cases cite incompatibility as the underlying reason. If ten couples file
for a divorce, what is the probability that:
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~,/(p Sa) ,Exa£tl~wo will state incompatibility as a reason? X -: ;).
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b) At least four couples will state incompatibility as a reason?
c)
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Less than four c?~ples will state incompatibility as a reasonl2..
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7. F..i",eJrundrecl,.pJ<ople
used a home test for HlV, and then all underwent more conclusive hospital testing.
The accuracy of the home test was evidenced in the following table. ,
Positive Test
HlV
35
•
Healthv
25
Negative Test
5
435
40
4&0
a) What is the probability that a person has.lllY and test JlQ~
b) What is theyrobability
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of testing )sitive
g~n
that the person does not h,ave HlV?
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c) What is the probability oftes!i.ng P9sitive glreg that the person has.HlY?
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8. The probability that a house in an urban area will be burglarized is 4o/~lf20
selected, what is the probabi!ity that:
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a) None of the house WIll be burglanzed?
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b) All of the houses will be burglarized?
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c) Three or less of the houses will be burglarized?
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9. A sales firm receives an average of three call~ per hour on its toll-~
the probability that it will recei':.e:
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a) -lhree
calls. X -
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b) Gre~t\lrJhan three calls.
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~(..J'-~s~rthreeyalls.
(,00' __ )
number~ For any given hour, find
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d) Greater than four of the houses will be burglarized?
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10. A company ships computer components in boxes that contain 20 items. Assume that the probability of a
defective computer component is_Q.2, Find the probability that the first defect is found
y.:'
a) In the s=th.component
tested. Round your answe to.four.decimal places.
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b) Not the first oneJmJ the second one. Round your answer to four decimal places.
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