HW3
solution
16. (2.1.10, pp.61)
(a) False. Sample proportion of defective items is an estimator of the probability of producing
defective item (from the process) with inherent variability.
(b) True. Same explanation as above.
(c) True. As the sample size increases, the variability of sample proportion will be alleviated and
the value of sample proportion will approach the true probability 10
17. Let
A
indicate the event that main data transmission channel functions and
B
for the backup channel
functioning, i.e P(
A
)=1
−
0
.
1=0
.
9
,
P(
B
−
0
.
15 = 0
.
85
,
and P(
A
∩
B
)=0
.
78.
P
(system works)
=
P(at least one functions) = P(
A
∪
B
)
add
.
rule
=P
(
A
)+P(
B
)
−
P(
A
∩
B
)
=0
.
9+0
.
85
−
0
.
78 = 0
.
97
.
18. (Draw venn diagram to assist your understanding) Let
L
indicates that salad contains lactose and
T
for tree nuts, i.e. P(
L
∩
T
c
.
05
,
P(
L
c
∩
T
.
07, and P(
L
∩
T
.
03,
(a) P(
L
∪
T
)=P(
L
∩
T
c
L
c
∩
T
LT
.
05 + 0
.
07 + 0
.
03 = 0
.
15
.
P(contains neither) = P(
L
c
∩
T
c
−
P(
L
∩
T
−
0
.
15 = 0
.
85.
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 Fall '11
 DANIELCONUS
 Statistics, Probability, Vehicle registration plate, sample proportion

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