NATIONAL
EXAMINATIONS
DECEMBER
2015
04
-BS
-2
1.A
review
of
the
extensive
data
available
in
the
files
of
Reliable
Tires
revealed
that
the
life
X
of
the
all-weather
tires
manufactured
by
the
company
is
a
normally
distributed
random
variable
with
mean
and
standard
deviation
equal
to
175,000kms
and
20,000kms
respectively.
(a)
Find
the
probability
that
the
life
of
a
randomly
selected
tire
lasts
less
than
190,0001(ms.
Write
down
the
probability
density
function
of
X.
Then
draw
the
probability
density
function
of
X,
neatly
and
clearly,
and
indicate
the
area
that
corresponds
to
this
probability.
(b)
Compute
the
probability
that
the
life
of
a
selected
tire
differs
from
the
mean
by
less
than
10,000kms.
Then
cipm
the
probability
density
function
of
X,
neatly
and
clearly,
and
indicate
the
area
(that
corresponds
to
this
probability.
(c)
Let
M
represent
the
average
life
of
a
random
sample
of
four
tires.
(i)
Find
the
mean
and
standard
deviationiiof
the
probability
distribution
of
M.
(ii)
Write
down
the
probability
density
function
of
M.
(iii)
Draw,
neatly
and
clearly,
the
probability
density
function
of
X
and
M
on
the
same
diagram.
(iv)
Compute
the
probability
that
M
exceeds
170,000
kms.
(d)
Mr.
Pinky,
the
owner
of
a
fleet
of
nine
limousines,
bought
a
set
of
36
tires.
Let
T
be
the
sum
of
the
lives
of
the
36
tires.
(i)
Write
down
the
probability
density
function
of
T.
(ii)
Compute
Ole
probability
that
T
exceeds
6,300,000kms
2.(A)
A
city-wide
survey
carried
out
on
behalf
of
the
Metropolitan
Council
of
a
large
urban
centre
revealed
that
60%
of
tkie
adult
inhabitants
of
that
centre
were
in
favour
of
extending
the
two
subway
lines
currently
available.
(a)
What
is
the
probability
that
in
a
random
sample
of
15
adult
inhabitants
more
than
five
but
fewer
than
nine
would
be
in
favour
of
that
extension?
(b)
What
is
the
probability
that
in
a
random
sample
of
12
adult
inhabitants
fewer
than
three
would
not
be
in
favour
of
that
extension?
(c)
A
leading
newspaper
carried,an
additional
survey
on
a
random
sample
of
4,000
adult
inhabitants.
Use
an
appropriate
approximation
to
compute
the
probability
that
fewer
than
2,450
were
in
favour
of
the
extension
under
consideration.
2.(B)
The
probability
that
a
member
of
a
large
professional
association
is
sued
for
malpractice
is
0.0015.
Use
an
appropriate
approximation
to
compute
the
probability
that
in
a
random
sample
of
2,000
members
more
than
two
were
sued
for
malpractice.
Explain,
briefly
and
clearly,
why
the
approximation
used
is
appropriate.
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