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Chaptera 5a Homework
Questiona 1:a Whicha typea ofa distributiona doesa thea grapha illustrate?
Uniforma distribution.
Questiona 2:a Whicha typea ofa distributiona doesa thea grapha illustrate?
Exponentiala distribution
Questiona 3:a whicha typea ofa distributiona doesa thea grapha illustrate?
Normala distribution
Questiona 17:a Ina thisa distribution,a outcomesa area equallya likely.a Whata doesa ita mean?
Thisa meansa thata thea valuea ofa xa isa likelya toa bea anya numbera betweena 1.5a anda 4.5a
Questiona 18:a Whata isa thea heighta ofa f(x)a fora continuousa probabilitya distribution?
𝑋~𝜇a (1.5, a 4.5)
F(x)=a 1/a (b-a)a fora a 𝑋~𝜇a (1.5, a 4.5)
F(x)a =a 1/a (4.5a -1.5)
F(x)a =a 0.333
Questiona 19:a Whata area thea constraintsa fora thea valuesa ofa x?
1.5a 𝑥a 4.5a
Questiona 25:a Finda thea probabilitya thata aa randomlya selecteda homea hasa morea thana
3,000a squarea feeta givena thata youa alreadya knowa thea housea hasa morea thana 2,000a
squarea feet.
𝑋~𝜇a (1.5, a 4.5)
F(x)a =a 1/a (4.5-a 2)a =1/2.5a fora 2<a x<a 4.5
P(x>a 3|a x>a 2)a =a (4.5a a 3)a (1/2.5)
=a 0.6
Questiona 29:a whata isa thea theoreticala mean?a
Theoreticala meana =a 6
Questiona 34:a whata isa beinga measureda here?
Agea ofa carsa ina yearsa
Questiona 46:a Whata typea ofa distributiona isa this?
Exponentiala distribution
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Questiona 58:a Whata isa thea cumulativea distributiona function?
Isa thea probabilitya functiona thea xa takes;a ina thisa casea cdfa =a 0.75
Questiona 64:a whata isa beinga measureda here?
Thea perioda (ina years)a ita willa takea toa decaya carbon-14
Questiona 65:a Area thea dataa discretea ora continuous?
continuous
Questiona 66:a Ina words,a definea thea randoma variablea X
Randoma variablea xa isa aa numericala descriptiona ofa thea outcomea ofa aa statisticala
experiment.a
Questiona 67:a whata isa thea decaya ratea (m)?
ma =a 0.000121
Questiona 73:a Whena agea isa roundeda toa thea nearesta year,a doa thea dataa staya
continuous,a ora doa theya becomea discrete?a Why?
Agea isa aa discretea regardlessa ofa thea accuracya ofa roundinga offa
Questiona 81:a Thea probabilitya ofa waitinga morea thana sevena minutesa givena aa persona
hasa waiteda morea thana foura minutesa isa
P(x>a 7|a x>4)
a 1/a (8-4)a =a ¼
Probabilitya isa 0.25
Questiona 83:a Supposea thata thea valuea ofa aa stocka variesa eacha daya froma $16a toa $25a
witha aa uniforma distributiona
a) Finda thea probabilitya thata thea valuea ofa thea stocka isa morea thana $19
F(x)a =a (1/a 25a a 1/16)
a F(x)a =a 1/9
P(x>a 19)a =a (25a a 19)a (1/9)a =a 2/3
b) Probabilitya betweena $19a anda $a 22
Pa (19a <a xa <a 22)
=a (22a a 19)a (1/9)a =a 1/3
c) Thea uppera quartilea 25%
25%a =a 0.25
0.25=x(1/9)
X=a (0.25)(9)
=a 2.25
Quartilea =a 25a a 2.25
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Quartilea =a 22.75
d) Givena stocka isa greatera thana $18a finda thea probabilitya thea stocka isa morea thana
$21
P(x>a 21|a x>a 18)
F(x)a =a 1/a 21a a 1/18a =a 1/7
P(x>a 21|a x>a 18)a =a (25a a 21)a 1/7
P(x>a 21|a x>a 18)a =a 4/7
Questiona 92:a Whata isa thea probabilitya thata aa phonea willa faila twoa yearsa ofa thea datea
ofa purchase
P(2<x<3)
Pa (x>2)a =a 1-a (1a -e^a (0.333*2))
=a 0.5137
Questiona 100:a
a) Finda thea probabilitya thata thea durationa betweena twoa successivea visitsa toa thea
websitea isa morea thana tena minutes
P(T<a t)=a 1a a e^(t/60)
=a 1a a e^a (-1/6)
=1-a 0.8464
=a 0.154
b) Thea topa 25%a ofa durationsa betweena visitsa area ata leasta howa long?
25%a =a 0.25
P(T<t)a =a 0.25
0.25a =a 1a a 163/t
Ta =a 122a minutes
c) Supposea thata 20a minutesa havea passeda sincea thea lasta visita toa thea website.a
Whata isa thea probabilitya thata thea nexta visita willa occura withina thea nexta 5a
minutes?
P(T>a 20|a T>a 5)
P(T>a 5)a =a 1a a (1-a e^a -(5/60)
=0.92
d) Finda thea probabilitya thata lessa thana 7a visitsa occura withina aa one-houra period?
Pa (X<a 7)
=a 1a a (1-a e^a (-7/60)
=a 0.8898
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