Transcript 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?
R unner 1 
2
 100%  16.7%
12
R unner 2 
3
25
 100%  12.0%
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
1
4
2

15
 93.75%
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
 97.22%  1 
36
1  .9722 
1
k
1
k
2
2
 97.22%
 .0278 
1
k
2
 k  36  k  6
2
6  .005  0.03  .260  .03  .290  .260  .03  .230
range  .230  .290 m illigram s
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) f
2
s
n 1

2287.5
79
 5.38
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 64

x

 16
x
(x - x)
(x - x)2
n
4
16.2
-0.2
.04
( x  x)
15.9
0.1
.01
15.8
0.2
.04
16.1
-0.1
.01
xx
.10
s
x = 64
n 1
2

 # s .d . 
0.10
 0.18
3
16  15.64
2
.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
60

n
11
-1
1
15
3
9
12
0
0
8
-4
16
14
2
4
n=5
x
x
30

s
 12
5
( x  x )  30
2

( x  x)
n 1
2

30
4
 2.74
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
-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
 
235

N
 19.6
12
2

586.92
 6.99
12
1 9 .6  6 .9 9  2 6 .5 9
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  m edian )
s

3(79.9  81.4)
  1.45
3.1
The scores are skewed negatively or to the left.