M3 Problem Set
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Course
110
Subject
Statistics
Date
Jan 9, 2024
Type
Pages
13
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M3:
Problem
Set
Due
No
due
date
Points
5
Questions
11
Time
Limit
None
Attempt
History
Attempt
Time
Score
LATEST
Attempt
1
149
minutes
5
out
of
5
Score
for
this
quiz:
5
out
of
5
Submitted
Dec
3
at
7:04pm
This
attempt
took
149
minutes.
Question
1
0/0pts
According
to
the
National
Oceanic
and
Atmospheric
Administration
(NOAA),
between
1851
and
2013
there
were
290
hurricanes
that
hit
the
U.S.
Coast.
Of
these,
117
were
Category
1
hurricanes,
76
were
Category
2
hurricanes,
76
were
Category
3
hurricanes,
18
were
Category
4
hurricanes,
and
3
were
Category
5
hurricanes.
Make
a
probability
distribution
for
this
data.
If
a
hurricane
hits
the
U.S.
coast,
what
is
the
probability
that
the
hurricane
will
be
a
Category
1
hurricane.
Your
Answer:
Category|Probability
1
117/290
=
0.403
76/290
=
0.262
76/290
=
0.262
18/290
=
0.062
5/290=
0.011
o~
ODN
There
is
a
.403
probability
that
it
will
be
a
category
1
hurricane.
Solution:
Category
Probability
117/290
=
403
76/290
=
262
76/290
=
262
18/290
=
.062
3/290
=
011
Q|
B
QO
N
—
We
can
see
from
the
probability
distribution,
that
if
a
hurricane
hits
the
U.S.
coast,
there
is
a
.403
probability
that
it
is
a
category
1
hurricane.
Question
2
0/0
pts
Find
the
answer
to
each
of
the
following
by
first
reducing
the
fractions
as
much
as
possible:
a)
P(17,8)=
b)
C(19,15)=
Your
Answer:
a)
P
(n,r)=n!/
(n-r)!
P(17,
18)
=
171/
(17-8)!
=
171/9!
=
17(16)(15)(14)(13)(12)(11)(10)
=
9
b)
C(n,
r)
=
n!/
rl(n-r)!
C(19,
15)
=
19!
/
151(19-15)
=
19!
/
15141
=
19(18)(17)(916)
/
4(3)(2)(1)
=
3876
Solution.
a)
For
permutations,
we
will
use:
n!
P(n,
r)
-
m
o
oSy
5
=
980,179,200
P(17,8)
=
ar—e)l_
o
17
(16)(15)(14)(13)(12)(11)(10)
=
,179,
b)
For
combinations,
we
will
use:
n!
i
i
ey
B
19!
_
190
19
(18)(17)(16)
_
€(19.15)
=
15!
(19
—15)!
15!4!
4(3)(2)(1)
3876
Question
3
0/0
pts
Suppose
you
are
going
to
make
a
password
that
consists
of
5
characters
chosen
from
{2,3,6,7,a,c,k,n,p}.
How
many
different
passwords
can
you
make
if
you
cannot
use
any
character
more
than
once
in
each
password?
Your
Answer:
Ordering
matters
P(n,
r)
=
N!/
(n-r)!
91/
(9
-
5)!
=
9!
/
41
=
9(8)(7)(6)(5)
=
15,120
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Solution.
For
passwords,
order
matters.
For
example,
the
password
63pn2
is
different
than
the
password
p2n36
even
though
both
passwords
use
the
exact
same
characters.
Therefore,
we
want
to
count
the
total
number
of
ways
that
we
can
choose
and
order
the
characters.
That
means
that
we
should
use
permutations.
We
have
a
total
number
of
nine
characters
to
choose
from,
so
n=9.
We
will
be
selecting
five
characters,
so
r=5.
We
will
use:
n!
P(n,r)
=
=)
!
9!
P(9,5)
=
@35
=
Fm
=
9(8)(7)(6)(5)
=
15,120.
Question
4
0/0
pts
Suppose
that
10
countries
submit
bids
for
the
summer
Olympics.
The
Olympic
committee
will
select
4
finalists
out
of
these
10
countries.
In
how
many
ways
can
the
Olympic
committee
pick
these
10
finalists?
Your
Answer:
Order
does
not
matter
C(n,
r)
=
n!'/
ri(n-r)!
10!
/
41(10-4)!
=
10!
/
416!
=
10(9)(8)(7)
/
4(3)(2)(1)
=
210
Solution.
Here
order
does
not
matter.
So,
we
will
use
combinations.
There
are
ten
countries
to
choose
from,
so
n=10.
Four
countries
will
be
chosen,
so
r=4.
We
will
use
Gl
rl
(n
-
r)!
10t
10t
10(9)(8)(7)
€104)
=
41
(10—-4)!
416!
4(3)(2)(1)
=
Question
5
0/0
pts
Suppose
A
and
B
are
two
events
with
probabilities:
P(A)
=.40,P(B)
=.45,P(AN
B)
=.25.
Find
the
following:
a)
P(A
U
B).
b)
P(A°).
c)
P(B°).
Your
Answer:
P(A)
=
.40,
P(B)
=
.45,
P(B)
-
25
a)
PAlU[B)
=
P(a)
+
P(B)
-
P(AINB)
40+.45-.25=.6
b)
P(A)=1-P(Ac)
converted
to
(Ac)=1-P(A)
1-.40=.60
C)
P(B)=1-P(Bc)
converted
to
(Bc)
=1-P(B)
P(Bc)=1-.45-55
Solution.
We
are
given:
P(A)
=
.40,
P(B)
=
.45,
P(AnB)
=.25.
a)
For
P(AUB).
Use
P(AUB)=P(A)+P(B)—P(ANB).
P(AUB)=40+
45-.25=
6.
b)
For
P(A°).
Use
P(A)
=
1
—
P(A®)
which
may
be
rearranged
to
(4°)
=1
-
P(4)
.
P(A®)
=
1
-
.40
=
.60.
c)
For
P(B¢).
Use
P(B)
=
1
—
P(B®)
which
may
be
rearranged
to
(B°)
=
1
—
P(B)
.
P(B€)
=1
-
.45
=
.55,
Question
6
0/0
pts
Suppose
A
and
B
are
two
events
with
probabilities:
P(A°)
=
.40,
P(B)
=
.25,
P(AUB)
=.75.
Find
the
following:
a)
P(ANn
B).
b)
P(A).
c)
P(B®).
d)
P((A
n
B)®).
Your
Answer:
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)
P(B)=P(A)+P(B)-P(AB)
converted
to
P(B)=P(A)+P(B)-P(A
o
P(A)=1-P(Ac)
so
P(A)=1-.40=.60
P(B)=.60+.25-.75=.1
b)
Found
above
P(A)=.60
C)
P(B)=1-P(Bc)
converted
to
(Bc)=1-P(B)
P(Bc)=1-25=.75
d)
P((Bc)‘c)=1-P(B)
1-.1=.9
Solution.
We
are
given:
P(A°)
=
40,
P(B)
=
.25,
P(AUB)
=.75
a)ForP(AnB).
Use
P(AUB)=P(A)+
P(B)—-
P(An
B)
and
rearrange
to
P(AnB)=P(A)
+
P(B)
—
P(A
U
B).
But
for
this
equation,
we
need
P(A4)
which
we
can
find
by
using
P(4)
=
1
—
P(A%).
So,
P(A)
=
1
—
.40
=
.60.
P(AnB)=.60+.25-.75=.1
b)
P(A)
was
found
above
as
.60.
c)
For
P(B¢).
Use
P(B)
=
1
—
P(B®)
which
may
be
rearranged
to
(B°)
=
1
—
P(B)
.
P(B°)
=1-25=.75.
d)
For
P((ANnB)®).Use
P((ANB)°)=1-P(ANB).
P((ANB)Y)=1-.1=.9.
Question
7
0/0
pts
Suppose
A
and
B
are
two
events
with
probabilities:
P(A)
=
.50,
P(B)
=
.40,
P(ANB)
=
.25.
a)
What
is
(A|B)
?
b)
What
is
(B|A4)
?
Your
Answer:
)
P(A|B)=P(B)
/P(B)
=
.25/.40
=
625
b)
P(B|A)=P(B)
IP(A)=.25/.50=.50
Solution.
We
are
given:
P(A)
=
.50,
P(B)
=
.40,
P(An
B)
=.25.
a)
For
P(A|B)
use
P(A|B)
=
5%;2
P(A|B)
=
f—i
o
£IE
b)
For
P(Bl4A)use
P(B|A)
=
it
P(B|A)
=
=2
50.
P(A)
50
Question
8
0/0
pts
Suppose
A
and
B
are
two
events
with
probabilities:
P(A°)
=
.30,
P(B|4)
=
.40.
Whatis(ANB)?
Your
Answer:
P(A)=1-P(
A®
)=P(A)=1-.30=.70
P(B|A)=P(AB)
IP(A)
converted
to
P(B)
=P(BIA)P(A)
P(B)
=(.40)(.70)=.28
Solution.
We
are
given:
P(A%)
=
.30,
P(B]A)
=
.40.
We
must
first
find
P(A).
By
using
P(A)
=
1
-
P(A°).
So,
P(4)
=1-.30=.70.
In
order
to
find
P(A
N
B),
we
can use
P(ANB
PlA)
P(BlA)
=
!
and
rearrange
to
get
P(An
B)
=
P(B|A)P(A).
So,
P(AnB)
=(.40)(.70)
=
.28.
Question
9
0/0
pts
Suppose
that
in
a
certain
type
of
washing
machine
that
the
probability
that
a
belt
will
fail
is
.03
and
the
probability
that
the
agitator
will
fail
is
.01.
The
probability
that
the
belt
and
the
agitator
will
fail
simultaneously
is
.008.
Suppose
that
you
discover
that
the
belt
in
a
washing
machine
failed,
what
is
the
probability
that
the
agitator
has
also
failed?
Your
Answer:
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A
=
event
agitator
will
fail,
B=
event
belt
fails
P(A)=.01,
P(B)=.03,
P(B)
=.008
P(A|B)=P(AB)
/P(B)
=.008/.03=.267
Solution
Suppose
that
in
a
certain
type
of
washing
machine
that
the
probability
that
a
belt
will
fail
is
.03
and
the
probability
that
the
agitator
will
fail
is
.01.
The
probability
that
the
belt
and
the
agitator
will
fail
simultaneously
is
.008.
Suppose
that
you
discover
that
the
belt
in
a
washing
machine
failed,
what
is
the
probability
that
the
agitator
has
also
failed?
Let’s
call:
B
the
event
that
the
belt
fails.
A
the
event
that
the
agitator
will
fail.
Then
P(A)
=
.01,
P(B)
=
.03,
P(A
N
B)
=.008
So,
the
probability
that
the
agitator
has
failed,
given
that
the
belt
has
failed
is
expressed
as:
P(AnB)
_
.008
P(AlB)
=
P(B)
03
=
.267.
Question
10
0/0
pts
In
a
manufacturing
plant,
three
machines
A,B,
and
C
produce
40
%,
35
%,
and
25
%,
respectively,
of
the
total
production.
The
company's
quality
control
department
determined
that
1
%
of
the
items
produced
by
machine
A,
1.5
%
of
the
items
produced
by
machine
B,
and
2
%
of
the
items
produced
by
machine
C
are
defective.
If
an
item
is
selected
at
random
and
found
to
be
defective,
what
is
the
probability
that
it
was
produced
by
machine
B?
Your
Answer:
"D"
to
designate
"Defective"
A
part
produced
by
machine
"A"
has
a
defect
probability
of:
P(D|A)=.01
A
part
produced
by
machine
"B"
has
a
defect
probability
of:
P(D|B)=.015
A
part
produced
by
machine
"C"
has
a
defect
probability
of:
P(D|C)=.02
We
are
told
the
probability
that
a
part
was
made
by
machine
"A"
"B",
"C"
are:
P(A)
=
0.40,
P(B)
=
0.35,
P(C)
=
0.25
We
need
to
find
P(B|D)
so
we
use:
P(B|D)=(.35)(.015)
/
(.40)(.01)+(.35)(.015)+(.25)(.02)
=
.368
Solution
In
a
manufacturing
plant,
three
machines
A,
B,
and
C
produce
40
%,
35
%,
and
25
%,
respectively,
of
the
total
parts
production.
The
company's
quality
control
department
determined
that
1
%
of
the
parts
produced
by
machine
A,
1.5
%
of
the
parts
produced
by
machine
B,
and
2
%
of
the
parts
produced
by
machine
C
are
defective.
If
a
part
is
selected
at
random
and
found
to
be
defective,
what
is
the
probability
that
it
was
produced
by
machine
B?
If
we
use Def
to
designate
“defective”.
We
are
told
that
given
that
a
part
was
produced
by
machine
A,
the
probability
that
it
has
a
defect
is:
P(Def
|A)
=
.01.
We
are
told
that
given
that
a
part
was
produced
by
machine
B,
the
probability
that
it
has
a
defect
is:
P(Def
|B)
=.015.
We
are
told
that
given
that
a
part
was
produced
by
machine
C,
the
probability
that
it
has
a
defect
is:
P(Def
|C)
=.02.
Furthermore,
we
are
told
that
the
probability
that
a
part
was
produced
by
machine
A,
B,
and
C,
are
respectively:
P(A)
=
.40,
P(B)
=
.35,
P
(C)
=
.25.
We
want
to
find
P
(
B
|Def),
so
use:
P(B)
=
P(Def|B)
P(B|Def)
=
(P(A)
™
P(DefIA))
+
(P(B)
*
P(Dele))
+
P(C)
=
P(DefIC).
.35+.015
=
.368.
P(BIDef)
=
o+
0T
+.35+.015+
25+.02
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Question
11
5/5
pts
As
a
reminder,
the
questions
in
this
review
quiz
are
a
requirement
of
the
course
and
the
best
way
to
prepare
for
the
module
exam.
Did
you
complete
all
questions
in
their
entirety
and
show
your
work?
Your
Answer:
Yes
Quiz
Score:
5
out
of
5
Related Questions
QUESTION 29
Add.
a.
b. 5
d.
e. 7
469
arrow_forward
A car knocked over a stop again, but then sped off. The only information that an eyewitness remembers is that the car’s license plates contains two W’s and one D, but not necessarily in this order. How many license plates must check?
arrow_forward
The average annual salary for 55 statisticians out of 205 statisticians at a search information company is $176,875. Which of the following best describes the bold-face number?
a. Quantile
b. Parameter
c. Statistic
d. range
arrow_forward
1. Favourite drink of 80 people
Other
Lemonade
Tea
Coke
Coffee
Drink
Degrees
Value
Tea
90
Coffee
180°
Coke
36
Lemonade
Other
18
1
person
degrees
(1 Marks)
arrow_forward
During which month were there 150 tornadoes?
Tornadoes per Month in Oklahoma
175
150
125
100
75
50
由25
Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.
Month
Enter
Tornado Frequency
arrow_forward
Question #1: What is the area of the composite figure below? DON'T
forget to.. *
2 in.
3 in.
9 in.
27 square inches
O 6 square inches
36 square inches
O Not Here
O O
arrow_forward
Grand Canyon...
arrow_forward
The first five rows of the BIRTHS data set are shown here. For GENDER 1 =male and 0 = female, WEIGHT is birth weight in grams, and CHARGES is in dollars. FACis facility, ADMIT and DISCHARGE are named days of the week.
FAC
INSURANCE
GENDER
ADMIT
DISCHARGE
WEIGHT
CHARGES
Albany
Medicaid
0
FRI
SUN
3500
13986
Albany
Blue Cross
1
FRI
SUN
3900
3633
Bellvue
Blue Cross
0
WED
THU
900
359091
Albany
Self Pay
1
MON
SAT
2800
8537
Olean
Medicaid
1
FRI
SUN
3700
3633
Describe the appropriate level of measure for each of the variables of the data. (Nominal,Ordinal, or Numerical - discrete, or Numerical - continuous).
arrow_forward
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Related Questions
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