Annual Incomes of 10 Families

1
Monthly Starting Salaries for a sample of 12
business school graduates
Graduate Monthly Starting Salary (TRL)
1 2,020
2 2,075
3 2,125
4 2,040
5 1,980
6 1,955
7 2,050
8 2,165
9 2,070
10 2,260
11 2,060
12 2,040
2
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
3
Find z-scores for each test, and state which is
higher.
Test A X38 Sample Mean40 St. Dev.5
Test B X94 Sample Mean100 St. Dev.10
4
Which score has the highest relative position.
A X12 Sample Mean10 St. Dev.4
B X170 Sample Mean120 St. Dev.32
C X180 Sample Mean60 St. Dev.8
5
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.
6
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.
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EMPIRICAL RULES 1- About 68 of the values will
lie within 1 standard deviation of the mean, that
is, between x - s and x s 2- About 95 of
the values will lie within 2 standard deviation
of the mean, that is, between x - 2s and x
2s 3- About 99.7 of the values will lie within
3 standard deviation of the mean, that is,
between x - 3s and x 3s
8
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?
9
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.
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