STAT 350 Assignment 1 Solutions (60pts)
11.
(a)
(4)
The following stemandleaf display was constructed using MINITAB
:
(It’s OK if the students
don’t include the first column in the following figure, i.e.
don’t cut off any point
if column of “12 23
(10) 14 7
5” is not included
but all the others are correct)
Stemandleaf of C1
N
= 47
Leaf Unit = 100
12
0 123334555599
23
1 00122234688
(10)
2 1112344477
14
3 0113338
7
4 37
5
5 23778
For “features of the display”,
give full credit if they make correct descriptions for number of peaks
(should be “unimodal” here)
and the direction of skewness.
A typical data value is somewhere in the low 2000's.
The display almost unimodal (the stem at 5
would be considered a mode, the stem at 0 another) and has a positive skew.
14.
(3)
For the first question, it’s OK if they haven’t mentioned the pattern of the values, give full credit as
long as they describe the peak (unimodal) and direction of skewness correctly.
A very large
percentage of the data values are greater than 0, which indicates that most, but not all, runners do
slow down at the end of the race.
The histogram is also positively skewed, which means that some
runners slow down a
lot
compared to the others.
And it
’s unimodal. (1 pt)
A typical value for this data would be in the neighborhood of 200 seconds.
(1 pt)
The proportion of the runners who ran the last 5 km faster than they did the first 5 km is very small,
about 1% or so. (1 pt)
18.
(a)
(1)
The classes overlap.
For example, the classes 2030 and 3040 both contain the number 30,
which happens to coincide with one of the data values, so it would not be clear which class to put this
observation in.
(b)
(2)
The histogram appears below:
1 0 0
9 0
8 0
7 0
6 0
5 0
4 0
3 0
2 0
1 0
0
3 0
2 0
1 0
0
C o n c e n t r a t i o n ( p p m )
R e la t i v e
f r e q u e n c y
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(c)
(2)
The proportion of the concentration values that are less than 50 is 17/50 = .34, or 34%.
The
proportion of concentrations that are at least 60 is 27/50
= .54, or 54%.
19.
(a)
(1)
The density curve forms a rectangle over the interval [4, 6].
For this reason, uniform densities
are also called
rectangular densities
by some authors.
Areas under uniform densities are easy to
find (i.e., no calculus is needed) since they are just areas of rectangles.
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 Spring '08
 Staff
 Statistics, Normal Distribution, Standard Deviation, Probability theory, probability density function

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