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MATH 1131 Midterm: MATH1131 Midterm Solution Version 2Exam


Department
Mathematics and Statistics
Course Code
MATH 1131
Professor
All
Study Guide
Midterm

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MATH 1131 MIDTERM
Wednesday,
October
27;
50
minutes
-
~
NAME:
_____
S_O_L!_U_f_IO_N_CS
________
_
STUDENT NUMBER:
___
H+\
I~_e
__
_
__\_(-'--H-O-P-~-~-I------·~
There are 5 questions
on
this test, worth a total
of
50 points. The questions are
in
no
particular
order.
Make sure that you show your work (when this is possible). When asked for comments in a ques-
tion, do so succinctly, and you may use point form if you wish.
We
will
be
looking for a correct
answer, not a lengthy answer.
The last page contains the probability distributions for discrete
RVs
and you may detach it from
the rest of the test.
You
may also use this page as scrap paper.
You
may write on the back
of
the
pages if you
run
out of space.
Good
Luck!

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

••
1. (2 marks each) Determine whether each of the following statements is true or false (write
T
or
F beside each statement). For these questions you do not need
to
show your work.
(a)
For a data set with a strongly right-skewed histogram, the sample mean will be
smaller than the sample median.
"
(b)
Suppose that we observe the outoome of three independent coin tosses. This is an
example of a random variable.
f
,-
(c) The current median income in Toronto is 23,000 annually. Suppose that the top 5%
of Toronto's population doubles its income, the bottom
5%
of the population halves
its income, and the income of the remaining population stays the same. Then the
median income is still 23,000.
(d)
Two
scatterplots for two different data sets are shown below.
You
know that the
correlations coefficients for the two data sets are 0.823 and -0.518, but you can't
remember which is which for sure. From looking at the plots, we can see that the
correlation for the one on the right must be 0.823, and for the one on the left must be
-0.518.
C!
'"
"l
..
"F
'"
~
"l
0
.-'
0.0 0.2 0.4 0.6 0.8
"1
'"
C!
OJ
"l
C!
••
-1.0
-0.5
0.0 0.5
T
(e)
Consider two events, A and
B.
The probability
of
event A is 0.6 and the probability of
event B is 0.7. It follows that the two events cannot be mutually exclusive.

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

--
2. A large cell phone company has three manufacturing plants: plants
A,
B,
and
C.
They
are concerned about the number of phones which are manufactured but are defective.
Plants A and B are well-established with good standards of practice, and only
3%
of
the
products they manufacture are defective. Plant C is relatively
new,
and 10%
of
its products
are defective. Suppose that 20%
of
the company's cell phones are manufactured in plant
A,
40% in plant
B,
and 40%
in
plant
C.
(a)
(4 marks) A cell phone is selected at random from the company's main warehouse.
What is the probability that it
is
defective?
reD)
::
0.2..-
0.01>
t o,'"{·
0.06
t
D.Lt
.
o.
\
-=-
O.
05~
(b)
(4
marks) Suppose that the cell phone sampled was not defective. What is the
probability that it came from plant C?
p
(e.
1
no-\"
D
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;,;.
:'0,'\.
{)
.'3"
L~o.eq,~
.-
..
.,
"
(c) (2 marks)
You
go
to the companies main warehouse and start selecting cell phones
at random. How many do you expect to select before you find your first defective
phone?
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