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Probability and Statistics for Engineering (ESE 326)
Exam2
March 22,2011
This exam contains 10 multiplechoice problems worth two points each, four truefalse problems worth
one point each, nine shortanswer problems worth one point each, and one freeresponse problem worth
seven points, for an exam total of 40 points.
Part
I.
MultipleChoice (two points each)
Clearly
fill
in the oval on your answer card which corresponds to the only correct response.
Corey's gerbils escape from their cage, on average, once every
four months. Use this information for the
first two
problems. (Assume, realistically,
that
this
is
a
Poisson process,
and also
assume,
unrealistically, that
all
months are
alike.
In other words, ignore the
unfortunate fact that different
months have different lengths.)
1.
Find the probability that the gerbils
will
escape at least three times during the year 2011.
(A)
.0022
(B)
.2381
(c)
.3528
(D)
.4232
(E)
.4335
(F)
.5665
,
t
AL+
(H)
.6472
(D
.76re
(J)
.ee78
S
=
l'Z
L
=
3
3l
:
lPfx:zJ
=
l
,123L
)F
t
r:t;
x
3
+]

;t+11
e/
(c)
.2473
(D)
.367e
(E)
.4724
(F)
.5276
(G)
.632r
(H)
.7587
(I)
.8e55
(J)
.eeee
PIz:
:
(t
=
*
(,
€
LD
)
I
=
Ll
F/x\
=
I

e
l>o
(')
*,
,l;r*"+
f)nu*o*
Pfx>
=
^
{taV
#*rr"^,
?nlo*^
2.
Find the probability that the first escape of
2011 happens during April.
(A)
.0001
{^
rL
d __
^
^
r+
i
+la
se
t
D+{
t4
e
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View Full DocumentSupposeXisacontinuousrandomvariablewithdensity
f
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n)
2. Find F(4).
(A)
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=
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=

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FU\=t
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SupposeXisacontinuousrandomvariablewithdensity
f
(*):22r,0<r
<
1. Find EIX'1.
4.
@
(B)
t
(c)
#
(D)
t
(E)
?
(F)
3
(G)
1
(H)
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5.
The life of the
AA batteries sold by
a particular corporation is
normally distributed with
a mean
of
2.5 hours and a standard deviation
of 0.3 hours. For
what battery
life (rounded to two
decimal
places) can the corporation claim lhatggYo of its
AA batteries last this long
or longer?
(Choose the
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