MTH 5102 Pretest C

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MTH 5102 Pretest C
1. Complete the following table
2. Knowing that the arithmetic mean of a group
in astronomy is 83 with a standard deviation of
3, what is Williams mark if he obtained a
standard score of -2?
3. Considering the fact Pascal and Isabelle
obtained the same result on a mathematics exam
and that the standard deviations of their
respective classes are 4 and 3, if Pascal has a
Z-score of -1 and Isabelle a Z-score of 2, which
class (Pascals or Isabelles) obtained the
higher mean? Explain.
The mean for Pascals class will be 4 more than
the mark that he and Isabelle obtained and the
mean for Isabelles class will be 6 less then
mark they obtained. Therefore Pascals class has
the higher mean.
2
4. Ludovic obtained a result of 16/20 on a
History test and another of 15/20 in French. In
History, the groups mean is 13.5/20 and in
French 12/20. The standard deviation for the
History class is higher that that of the French
class. For which subject did Ludovic have the
best performance compared to the remainder of the
class?
If the standard deviation for the History class
is greater then his standard score in History has
to be less than for French which makes his
performance in French better.

• Two javelin throwers record their daily best over
  a 10 day period as they train for a competition.
  The results are in the table below.
• Which athlete is better prepared for the
  competition? Explain

Joe is better prepared because his mean is
slightly higher at 89 versus 87.2 for Ben. Also
his results are much more consistent with a
standard deviation of 3.16 compared 7.60 for Ben.
3

• All students from adult education are submitted
  to a general knowledge test. To do so, they are
  separated into 6 groups with each group receiving
  a different test. After the test, the director
  wants to give a special award to the best
  performance.

What group will the award winner come from?
The award winner comes from Group B as the person
with the best mark in that group had the highest
standard score of all groups with a Z-score of 3.
4

• Match each scatter plot to its corresponding
  correlation correlation coefficient.

• Identify the direction (positive or negative) and
  the degree of the correlation characterizing the
  following statements.
• A) A persons annual salary and the length of
  his nose.
• B) The distance traveled by a car and the
  amount of gas left in his tank.
• C) The number of practice hours for a driving
  exam and the result obtained for this exam.
• D) The link between the number of nice weather
  days and the amount of precipitation each year.
• E) The number of hours worked per week and the
  salary of a person.

A Not Significant B Strong Negative C
Strong Positive D Moderate Negative E Perfect
Positive
5

• Use the rectangular method to estimate the value
  of the correlation coefficient for the following
  scatter plot.

Ages of couples from Beauport
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10. Considering the following scatter plot and
the following means
(56.8,58.15)
(52,53)
a) Determine the equation of the regression line
for this distribution from the scatter plot.
y 1.073x a 53 1.073(52) a 53
55.79 a a -2.79
y 1.073x 2.79
b) Use the equation of the regression line to
determine the result a student got in his retake
if he got 51 on his original exam.
y 1.073(51) 2.79 y 54.723 - 2.79
y 51.9
According to the equation of the regression line
the student should get 52 on the retake.
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11. The following table presents the best
rookies in the history of the NBA. Give the
degree and justify the correlation that exists
between the age of a player during his first year
and the average points scored per game by that
player during that year.
The correlation coefficient is 0.414 which means
that there is a very weak positive correlation
between the age of a rookie player and the number
of points he scores per game in his rookie
season. In fact, it is very close to being not
significant.
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12. The following table shows the demographic
projections of the UN concerning the population,
fertility rate and the percentage that is over 60
years old for certain countries according to a
estimate in the year 2000 .
For the Population and Fertility Rate r
0.5083 and y 400.3845x 424.4044
For the Population and Percentage over 60 years
old r -0.6437 and y -43.8003x
1049.7626
a) In order to get the best estimation of the
population, which of the above two models would
be preferable to use? Why? b) Determine the
fertility rate for Spain which has a population
of 40 000 000 inhabitants. c) Determine
Swedens population given that 18.3 of its
population is over 60 years old.
The best estimation of population can be
determined from the percentage over 60 years old
because it is the strongest and therefore most
significant correlation. i.e. furthest from 0
y 400.3845x 424.4044 40 400.3845x
424.4044 40 424.4044 400.3845x 400.3845x
464.4044 x 1.16
y -43.8003x 1049.7626 y
-43.8003(18.3) 1049.7626 y -801.5455
1049.7626 y 248
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13. Below is a table expressing the number of
alcoholic drinks a 70 kg man consumes and the
number of mg of alcohol detected in a blood
sample at a given time after..

• What is the correlation coefficient between these
  2 variables?
• Determine the equation of the regression line.
• Can you assert that a prediction made using this
  line is reliable?
• If this tendency continues, how many mg of
  alcohol will be in a blood sample after 12 drinks?

r 1
y 29x
Yes, in fact it is a perfect correlation so it is
as reliable as it can ever possible be.
y 29x y 29(12) y 348 mg
After 12 drinks I would expect 348 mg of alcohol
in a blood sample.
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14. The UN compares life expectancy for several
countries in the year 2000 with the projections
for the year 2050 in the following table.
Life Expectancy

• Does a statistic relationship exist between the
  life expectancy in a country for the year 2000 to
  that in the year 2050? If so, qualify it?
• Is the following table interesting for a
  statistician? Why?

Yes, a statistical relationship does exist
between the life expectancy in 2000 with that in
2050 with a very strong positive correlation (r
0.9593). The relationship can be expressed by the
following equation of its regression line y
0.7364x 25.56
Whenever there is a strong correlation, it makes
for an interesting relationship because it allows
for predictability and also can lead to
investigating whether relationships exists
between other similar variables.