Transcript Annual Incomes of 10 Families

A testing lab wishes to test two experimental brands of outdoor paint to see how long each
will last before fading. Two groups from different agents are formed with 6 cans of each.
The results (in Months) are shown:
Brand A
Brand B
10
35
60
45
50
30
30
35
40
40
20
25
A student scored 65 on statistics test that had a mean of 50 and a standard deviation of
10, she scored 30 on history test with a mean of 25 and a standard deviation of 5.
Compare her relative positions on the two tests
Find z-scores for each test, and state which is higher.
Test A:
X=38
Sample Mean=40
St. Dev.=5
Test B:
X=94
Sample Mean=100 St. Dev.=10
Which score has the highest relative position.
A
X=12
Sample Mean=10
St. Dev.=4
B
X=170
Sample Mean=120 St. Dev.=32
C
X=180
Sample Mean=60
St. Dev.=8
Problem
The table lists means and standard deviations. The results are from a study attempting to
find average blood pressure of older adults. The mean is the number before ± and The
standard deviation is the number after ±
NORMOTENSIVE
Age
HYPERTENSIVE
Men
Women
Men
Women
n=1200
n=1400
n=1100
n=1300
55±10
55±10
60±10
64±10
121±11
153±17
156±20
76±7
91±10
88±10
Blood Pressure (mm HG)
Systolic 123±9
Diastolic 78±7
Apply Chebyshev’s theorem to systolic blood pressure of normotensive men.
Q-1: At least how many of the men in the study fall within 1 standard deviation of the mean?
Q-2: At least how many of the those men in the study fall within 2 standard deviation of the mean?
Assume that blood pressure is normally distributed among older adults. Answer the following questions,
using the empirical rule (for 95%) instead of Chebyshev’s theorem.
Q-3 Give ranges for the diastolic blood pressure (normotensive and hypertensive) of older women.
Q-4 Do the normotensive, male, systolic blood pressure ranges overlap with the hypertensive, male
systolic, blood pressure ranges?
The mean price of houses in a certain neighborhood is 50,000 USD and standard
deviation is 10,000 USD. Find the price range for which at least 75% of the houses will
sell.
A survey of local companies found that the mean amount of travel allowances for
executives was 0.25 USD per mile. The standard deviation was 0.02 USD. Using
Chebyshev`s Theorem find the minimum percentage of the data values that will
fall between 0.20 USD and 0.30 USD.
Table: Ordered Array of Aptitude Test Scores for 40 Job Applicants.
∑x=2338 and ∑x2=157262
App.
Grade
App.
Grade
App.
Grade
App.
Grade
1
20
11
42
21
56
31
78
2
21
12
43
22
58
32
80
3
23
13
43
23
59
33
81
4
25
14
46
24
61
34
85
5
30
15
48
25
62
35
90
6
35
16
50
26
65
36
92
7
36
17
51
27
68
37
96
8
39
18
52
28
70
38
98
9
40
19
54
29
71
39
99
10
41
20
55
30
75
40
100
Why do we need the standard deviation?
1- The standard deviation reflects dispersion of data values,
so that the dispersion of different distributions may be
compared by using standard deviations.
2- The standard deviation permits the precise interpretation of
data values within a distributions.
3- The standard deviation, like the mean, is a member od a
mathematical system which permits its use in more advanced
statistical considerations.
EMPIRICAL RULES
1- About 68% of the values will lie within 1 standard deviation of the mean, that
is, between x̄ - s and x̄ + s;
2- About 95% of the values will lie within 2 standard deviation of the mean, that
is, between x̄ - 2s and x̄ + 2s;
3- About 99.7% of the values will lie within 3 standard deviation of the mean,
that is, between x̄ - 3s and x̄ + 3s;
Problem
Based on a survey of dental practitioners, the study reported that the mean
number of units of local anesthetics used per week by dentists was 79, with a
standard deviation of 23. Suppose we want to determine the percentage of
dentists who use less than 102 units of local anesthetics per week.
a- Assuming nothing is known about the shape of the distribution for the data,
what percentage of dentists use less than 102 units of local anesthetics per
week?
b- Assuming that the data has a mound-shaped (bell-shaped or symmetric)
distribution, what percentage of dentists use less than 102 units of local
anesthetics per week?
Problem
Based on the study to compare the effectiveness of washing the hands with
soap and rubbing the hands with alcohol-based antiseptics.
Table: Descriptive statistics on bacteria counts for the two groups
of health care workers.
Mean
Standard Deviation
Hand rubbing
35
59
Hand washing
69
106
a- For hand rubbers, form an interval that contains at least 75% of the bacterial
counts.
b- For hand washers, form an interval that contains at least 75% of the bacterial
counts.
(Note that the bacterial count cannot be less than 0)
c- On the basis of your results in parts a and b, make an inference about the
effectiveness of the two hand cleaning methods.