STAT 1000 Assignment 3
DUE:
February 29th (Wed. Eve. Section), March 1st (T/Th. Sections),
March 2nd (MWF. Sections)
SHOW ALL YOUR WORK
1.
[4]
A variable
X
has a distribution which is described by the density curve shown below:
(a) What proportion of observations of
X
are less than 5?
Solution:
The area of the rectangle (base * height) between 2 and 5 is (5

2)(0
.
2) = 0
.
6
and the area of the rectangle less than 2 is (2

0)(0
.
1) = 0
.
2.
Therefore, summing them the proportion of observations less than 5 is 0.8.
(b) What proportion of observations are between 2 and 4?
Solution:
The area of the rectangle between 2 and 4 is: (2)(0
.
2) = 0
.
4
2.
[2]
A random variable
X
has a triangular distribution on the interval 5 to 10. What must
the height be in order for this to be a true density curve?
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Solution:
The area of a triangle is
(
b
)(
h
)
2
. We know the area under all density curves is equal
to 1.
Therefore, 1 =
(10

5)(
h
)
2
,
h
=
2
5
3.
[1]
A telemarketing firm in a certain city uses a device that dials residential telephone
numbers in that city at random.
Of the first 100 numbers dialed,
51%
are unlisted.
This is not surprising because
48%
of all residential phone numbers in this city are
unlisted. Explain whether the percentages in
bold
are either a statistic or parameter.
Solution:
51%
is the
statistic
, this value is obtained from the sample.
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 Spring '12
 XU
 Normal Distribution, Standard Deviation, JeanBaptiste Grange

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