CEE110_PS5_2016
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Transcript of CEE110_PS5_2016
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CEE 110 Probability and Statistics for EngineersProblem Set 5
Due Thursday of Week 7, 10 a.m.
Read sections 8-1, 8-2, and 8-4, and comp ete!
8-4, 8-12, 8-14, 8-17, 8-2", 8-40, 8-#1, 8-#"
$ractice pro% ems &p ease re'ie()!
8-" a) *amp e mean from the +rst con+dence inter'a 8.02 ./8-8.02) 2 "0
*amp e mean from the second con+dence inter'a /./" .0"-/./") 2 "0
%) The /" 3 is & 8.02, #1./8) and the /0 3 is & /./", #0.0"). Thehi her the con+dence
e'e , the (ider the 3.
8-11 /" T(o-sided 3 on the true mean yie d! (here 5 /0.480, σ ,n " and 6 0.02" 1./#
11.9385.875/)3(96.1480.905/)3(96.1480.90
// 025.0025.0
≤≤
+≤≤−
+≤≤−
µ
µ
σ µ σ n z xn z x
8-1 a) // T(o-sided 3 on the true mean piston rin diameter or α 0.01, 6 α 2 6 0.00" 2."8 , and 5 74.0 #, σ 0.001, n 1"
x z
nx z
n−
≤ ≤ +
0 005 0 005. .σ µ σ
74036 258
0001
1574036 258
0001
15. .
.. .
.−
≤ ≤ +
µ
74.0 " ≤ µ ≤ 74.0 #7
%) // ne-sided 3 on the true mean piston rin diameteror α 0.01, 6 α 6 0.01 2. and 5 74.0 #, σ 0.001, n 1"
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787.225,005.0 =t 385.330,001.0 =t
8- / a) The data appear to %e norma y distri%uted %ased on e5amination ofthe norma pro%a%i ity p ot %e o(.
%) /" t(o-sided con+dence inter'a on mean comprehensi'e stren th
35.62259.912 === s xn 201.211,025.0 =t
5.22823.223712
6.35201.29.2259
12
6.35201.29.2259
11,025.011,025.0
≤≤
+≤≤
−
+≤≤
−
µ
µ
µ n
st x
n
st x
c) /" o(er-con+dence %ound on mean stren th
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µ
µ
µ
≤
≤
−
≤
−
4.2241
12
6.35796.19.2259
11,05.0n
st x
8-#2 a) /" on+dence 3nter'a on the death rate from un cancer.
823.01000823ˆ == p
1000=n 96.12/ =α z
8467.07993.01000
)177.0(823.096.1823.0
1000)177.0(823.0
96.1823.0
)ˆ1(ˆˆ)ˆ1(ˆˆ 2/2/
≤≤
+≤≤−
−+≤≤−−
p
p
n p p
z p pn
p p z p α α
%) 9 0.0 , α 0.0", 6 α 2 6 0.02" 1./# and p 0.82 as the initiaestimate of p,
79.621)823.01(823.003.096.1
)ˆ1(ˆ22
2/ =−
=−
= p p E
z n α
,n ≅ #22.
c) 9 0.0 , α 0.0", 6 α 2 6 0.02" 1./# at east /" con+dent
11.1067)25.0(03.096.1
)25.0(22
2/ =
=
= E
z n α
,n ≅ 10#8.
8-## 9 0.017, α 0.01, 6 α 2 6 0.00" 2."8
13.5758)5.01(5.0017.0
58.2
)1(
222/
=−
=−
= p p E z
n α
, n ≅ "7"/
