Section 36
361.
A binomial distribution is based on independent trials with two outcomes and a constant probability of
success on each trial.
a) reasonable
b) independence assumption not reasonable
c) The probability that the second component fails depends on the failure time of the first component.
The
binomial distribution is not reasonable.
d) not independent trials with constant probability
e) probability of a correct answer not constant.
f) reasonable
g) probability of finding a defect not constant.
h) if the fills are independent with a constant probability of an underfill, then the binomial distribution for
the number packages underfilled is reasonable.
i) because of the bursts, each trial (that consists of sending a bit) is not independent
j) not independent trials with constant probability
362.
(a) P(X
≤
3) = 0.411
(b) P(X>10) = 1 – 0.9994 = 0.0006
(c) P(X=6) = 0.1091
(d) P(6
≤
X
≤
11) = 0.9999 – 0.8042 = 0.1957
363.
(a) P(X
≤
2) = 0.9298
(b) P(X>8) = 0
(c) P(X=4) = 0.0112
(d) P(5
≤
X
≤
7) = 1  0.9984 = 0.0016
364.
a)
2461
.
0
)
5
.
0
(
5
.
0
5
10
)
5
(
5
5
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
=
X
P
b)
8
2
9
1
10
0
5
.
0
5
.
0
2
10
5
.
0
5
.
0
1
10
5
.
0
5
.
0
0
10
)
2
(
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
≤
X
P
0547
.
0
)
5
.
0
(
45
)
5
.
0
(
10
5
.
0
10
10
10
=
+
+
=
c)
0107
.
0
)
5
.
0
(
5
.
0
10
10
)
5
.
0
(
5
.
0
9
10
)
9
(
0
10
1
9
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
≥
X
P
d)
6
4
7
3
5
.
0
5
.
0
4
10
5
.
0
5
.
0
3
10
)
5
3
(
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
=
<
≤
X
P
3223
.
0
)
5
.
0
(
210
)
5
.
0
(
120
10
10
=
+
=
365.
a)
(
)
8
5
5
10
40
.
2
99
.
0
01
.
0
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 Spring '10
 Feng
 Probability theory, Binomial distribution, Decimal, 0.999...

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