Download Chapter 2 Review Problems

Chapter 2 Review Problems
Supplement of problems for Q3 Exam
Chapter 2 Supplemental Problems
During the past few months, one runner averaged 12 miles per week with a standard
deviation of 2 miles, while another runner averaged 25 miles per week with a
standard deviation of 3 miles. Which of the runners using the coefficient of variation
is relatively more consistent in his weekly running habits?
2
 100%  16.7%
12
3
Runner 2   100%  12.0%
25
Runner1 
Since 12.0% is less than 16.7%,
the second runner is relatively
more consistent in his weekly
running habits.
Chapter 2 Supplemental Problems
According to Chebyshev’s Theorem, what can we assert about the percentage of any
data set that must lie within k standard deviations on either side of the mean when k = 4?
1 15
1 2 
 93.75%
4 16
93.75% of the data must lie within 4
standard deviations on either side of the
mean.
A study of nutritional value of a certain kind of bread shows that on the average one
slice contains 0.260 milligrams of vitamin B1 with a standard deviation of 0.005
milligram. According to Chebyshev’s Theorem, between what values must the vitamin
B1 content be of at least 35/36 slices of this bread?
35
1
 97.22%  1  2  97.22%
36
k
1
1
1  .9722  2  .0278  2  k 2  36  k  6
k
k
6  .005  0.03  .260  .03  .290  .260  .03  .230
range  .230  .290milligrams
Chapter 2 Supplemental Problems
The amount of time 80 students spend on leisure activities each week. Calculate the
standard deviation of this group. (Grouped Data – Standard Deviation Problem)
x
Hours
Freq.
(f)
Midpt
(x)
xf
x -x
(x -x)2 (x -x)2f
10-14
8
12
96
-8.69
75.52
604.16
15-19
28
17
476
-3.69
13.62
381.36
20-24
27
22
594
1.31
1.72
46.44
25-29
12
27
324
6.31
39.82
477.84
30-34
4
32
128
11.31 127.92 511.68
35-39
1
37
37
16.31 266.02 266.02
f=80
x
1655
1655
 20.69
80
( x  x) 2 f
2287.5
s

 5.38
n 1
79
524.62 2287.5
Chapter 2 Supplemental Problems
A filling machine in a high-production bakery is set to fill open-faced pies with 16
fluid ounces of filling for each pie. A sample of four pies from a large production lot
showed fills of 16.2, 15.9, 15.8, and 16.1 fluid ounces. Calculate the standard
deviation. What percentage of the pies will have fill values between 15.64 and
16.36?
(x - x)
(x - x)2
16.2
-0.2
.04
15.9
0.1
.01
15.8
0.2
.04
16.1
-0.1
.01
x
x = 64
.10
x 64

x

 16
n
4
( x  x) 2
0.10

 0.18
n 1
3
xx
16  15.64
 # s.d . 
2
s
.18
2 standard deviations from the mean
equals 95% of the data. 95% of the pies
filled will be within this range.
Chapter 2 Supplemental Problems
In five attempts, it took a person 11, 15, 12, 8, and 14 minutes to change a tire on
a car. Determine the sample standard deviation.
Times of
Attempt
(x - x)
(x - x)2
n
11
-1
1
15
3
9
12
0
0
8
-4
16
14
2
4
n=5
x 60

x

 12
30
5
2
(
x

x
)
 30

s
2
(
x

x
)

n 1
30

 2.74
4
Chapter 2 Supplemental Problems
The following are the numbers of hours that 12 students studied for a final
examination: 7, 14, 22, 19, 20, 13, 25, 28, 32, 11, 20, and 24. Determine the
standard deviation of this population. How many scores are above 1 standard
(x - ) (x - )2
deviation?
x 235



 19.6
-12.6
158.76
-5.6
31.36
2.4
5.76
-0.6
0.36
0.4
0.16
 (x  )
-6.6
43.56
N
5.4
29.16
8.4
70.56
12.4
153.76
-8.6
73.96
0.4
0.16
4.4
19.36
586.92
N
12
2

586.92
 6.99
12
19.6  6.99  26.59
There are 2 scores above one
standard deviation; 28, 32.
Chapter 2 Supplemental Problems
On a final examination in a Statistics course, the mean grade is 79.9, the
median grade is 81.4, and the standard deviation is 3.1. Determine the Pearson
coefficient of skewness.
P
3( X  median) 3(79.9  81.4)

 1.45
s
3.1
The scores are skewed negatively or to the left.