Math 150
Final Exam
Spring 2007
City College of New York
Answer nine complete questions. Omit three complete questions. Show all work for part credit.
Be sure to include appropriate units and round to two decimal places unless otherwise indicated.
1. a) Draw a labeled Venn diagram to test the validity of the following argument and state
whether or not the argument is valid. Also, discuss whether or not the argument is sound.
Premises:
All birds have feathers. All sparrows have feathers.
Conclusion:
All sparrows are birds.
(7 pt.)
b) A population of coelacanths grows at the rate of 1.4% a year. Find the approximate time for
the population to double.
(4 pt.)
2. a) There are twenty million microchips in a box and each microchip weighs 0.00073 grams.
Find the total weight of the microchips in one box by changing both numbers to scientific
notation before doing your calculation. Give your answer in ordinary notation.
(6 pt.)
b) During 2006, the wholesale price of wheat fell from $5.25 per bushel to $4.37 per bushel.
Find the absolute change and the relative change (as a percent correct to two decimal places) in
the price of a bushel of wheat.
(5 pt.)
3. a) Property taxes in Metropolis have increased by 28% in the past year. If the average
homeowner pays $4275 this year, what did (s)he pay last year?
(5 pt.)
b) The price of a new computer is $1200 today and it decreases at the rate of $30 a month.
Let P = the price of the computer (in $) and let t = time after today (in months.) (6 pt.)
i) Write an equation expressing P as a function of t.
ii) Find the price of the computer 1 year from today.
iii) Find in how many months the price of the computer will be $1060.
4. a) The following table describes the educational level of smokers in the U.S.
Less than a high
school diploma
High School
Graduate
Some college
College graduate
35%
28%
20%
17%
i) Draw an appropriate graph, labeling carefully, to represent the above data.
ii)If there are 56 million people in the U.S. that are smokers, find the number of smokers
that have attended college.
(8 pt.)
b) When confronted with questions from the press about alleged political scandals, a
congresswoman replies that the allegations against her should be ignored since her accuser is
part of a vast right-wing conspiracy. Describe the fallacy.
(3 pt.)
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Math 150 Final Exam Spring 2007
page 2
5. a) Assume that you breathe on average once every ten seconds. How many breaths do you
take in 12 weeks? You must show the use of units.
(6 pt.)
b) Explain what is meant by “selection bias” in a study.
(5 pt.)
6. a) Given the conversions listed below, find how many Japanese yen there are in 1 Mexican
peso, correct to two decimal places.
(6 pt.)
1 American dollar = 119.35 Japanese yen
b) Consider the argument:
Premises:
and
1 American dollar = 10.93 Mexican pesos.
If Fluffy is a poodle then Fluffy is a dog.
Fluffy is not a poodle
Fluffy is not a dog.
Conclusion:
Is the above argument valid? Justify your answer by either naming the form of the argument,
through a diagram or through an explanation.
(5 pt.)
7. a) The population of Dystopia, NJ was 83,000 in 1991 and decreases by 7.2% each year.
Find the population in 2007.
(6 pt.)
b) Describe the difference between an observational study and an experimental study. (5 pt.)
8. a) What is the cost of lighting a 500-watt outdoor light for 8 hours if electricity cost 13.5
cents per kilowatt-hour?
(5 pt.)
b) Find the mean, median and the mode of the following data:
1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7
(6 pt.)
9. The weights of adult black bears are normally distributed with a mean (and median) of 135
kilograms and a standard deviation of 20 kilograms
a) Explain how you know the percentage of adult black bears that weigh 135 kilograms or
more without doing any calculation.
b) Find the percentage of adult black bears that weigh between 114 and 159 kilograms.
c) If 350 adult black bears were weighed, how many of them would weigh less than 150
kilograms?
10. a) In an experiment on the effects of a drug on reaction time, a subject is asked to depress a
button whenever a light flashes. Her reaction times for 13 trials are:
101, 96, 101, 102, 138, 93, 99, 107, 95, 95, 100, 100, 99
Find the five number summary for these data and draw a labeled box (box and whiskers) plot
for these data. Are there any outliers? If so, identify.
(9 pt.)
b) Find the negation of the statement:
Some dogs are dangerous.
(2 pt.)
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Math 150 Final Exam Spring 2007
page 3
11. a) A company that manufactures fruit-flavored beverages tests two new flavors (kiwi and
pomegranate) on 320 people. They find 200 people like the pomegranate beverage, 172 like
the kiwi beverage and 144 people like both beverages.
i) Draw a labeled two-circle Venn diagram to represent this information
ii) Calculate how many people in the study do not like either beverage.
(7 pt.)
b) On a map, 44 kilometers are represented by 5 centimeters. Find the scale ratio.
(4 pt.)
12. The graph given below shows the health expenditures per person for seven countries as well
as the life expectancy at birth for those countries.
a) What percent of the health expenditure per person in Japan is the health expenditure per
person in the United States?
b) On average, how much longer does a person living in Switzerland live than a person living
in Mexico? Express the answer as an absolute difference and as a relative difference (as a
percent.)
c) The American Medical Association claims that if we had a higher health expenditure per
person in this country, U.S. citizens would have the highest life expectancy of any country. Do
the data in the graph support this assertion? Explain.
HEALTH EXPENDITURE PER PERSON
2003, in U.S. dollars adjusted for inflation
Life expectancy at birth, 2004
$6,252
United States 77.9
Switzerland 81.2
$4,211
France 78.6
$3,337
Germany 78.6
$3,290
Sweden 80.6
$3,005
Japan 82.1
$2,462
Mexico 75.2 $666
$-
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
END
(Please look on the back of this sheet for the normal table.)
Good Luck!