SOLVED EXERCISES FROM THE ECONOMICS BOOK Anderson, Sweeney and Williams
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ScribdTranslationsSOLVED EXERCISES FROM THE ECONOMICS BOOK Anderson, Sweeney and Williams
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ScribdTranslationsJUAREZ UNIVERSITY
AUTONOMOUS
TABASCO
Academic Sciences Division
Economic Administrative
Subject : Probability and
statistics
Professor : PhD Leonel Valencia
Avalos
Student : Blanca Odette
Hernández
Rivera
Group : 2nd "OR"
Delivery date: Friday 24th
April 2020
“ Study in doubt, action in
Instructions
Solve exercises 1 -13
EXERCISES
1. An experiment consists of three steps; For the
first step there are three possible outcomes, for the
second there are two possible outcomes, and for
the third step there are four possible outcomes.
How many different results are there for the entire
experiment?
(3)(2)(4)=24
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2. In how many ways is it possible to select three
objects from a set of six objects? Use the letters
A, B, C, D, E and F to identify the objects and list
all different combinations of three objects.
3. How many permutations of three objects can
be selected from a group of six objects? Use the
letters A, B, C, D, E, and F to identify the objects
and list each of the feasible permutations for
objects B, D, and F.
2.EFD 4.VBE 6 FVB
4. Consider the experiment of flipping a coin three
times.
to. Make a tree diagram of this experiment.
b. List the results of the experiment.
11 1 mu 111 nun mui mili i
5. Suppose an experiment has five equally possible
outcomes: E1, E2, E3, E4, and E5. Assign probabilities to
the results and show that they satisfy the requirements
expressed by equations (4.3) and (4.4). What method did
you use?
6. An experiment that has three outcomes is
repeated 50 times and it is seen that E1 appears 20
times, E2 13 times, and E3 17 times. Assign
probabilities to outcomes. What method did you
use?
7. The decision maker assigns the following
probabilities to the four outcomes of an
experiment: P(E1) 0.10, P(E2) 0.15, P(E3) 0.40, and
P(E4) 0.20. Are these probability assignments
valid? Argue.
Applications
8. In a city, land use change requests go through a two-step
process: a review by the planning commission and the final
decision made by the city council. In step 1 the planning
commission reviews the land use change request and makes a
positive or negative recommendation regarding the change. In
Step 2 the city council reviews the recommendation made by the
planning commission and votes to approve or disapprove the
land change. Suppose that a company dedicated to the
construction of apartment complexes submits a request for a
change of land use. Consider the application process as an
experiment. How many sample points does this experiment
have? List them. Construct the tree diagram of the experiment.
9. Simple random sampling uses a sample of size n taken
from a population of size N to obtain data to make
inferences about the characteristics of the population.
Suppose that, from a population of 50 bank accounts, you
want to take a sample of four accounts in order to have
information about the population. How many different
samples of four accounts can they get?
—.N-5O P: _ sol' • ¿
____n\(pM)\ 461 ~ ~
3.04140932*106—
(24)(5,.S0262216x1057
N=sO f S 0\ SOI SOI (So)(49/49)(47) ne4 <4 ) 41(50-4)%
*4146 ' (4)(3)(2)(1)
10.Venture capital is a strong help for companies' available funds. According
to Venture Economics (Investor's Business Daily, April 28, 2000) of 2,374
venture capital disbursements, 1,434 are from companies in California, 390
from companies in Massachusetts, 217 from companies in New York, and 112
from companies in Colorado. Twenty-two percent of companies receiving
funding are in the initial stages of development and 55% are in the expansion
stage. Suppose you want to randomly pick one of these companies to see how
venture capital funds are used.
a. What is the probability that the company you select is from
California?
b. That the company is not from any of the states mentioned?
c. That the chosen company is not in the initial stages of development?
d. If you allow that companies in the early stages of development were
evenly distributed across the country, how many Massachusetts
companies that receive venture capital funding are in the early stages of
c. 100-22- 79 -» 0-18_________
development?
e. The total amount of funds invested is $32.4 billion. Estimate the
amount going to Colorado.
EXERCISES............................................................................................................................2
(3)(2)(4)=24.........................................................................................................................2
11 1 mu 111 nun mui mili i.........................................................................................................4
—.N-5O P: _ sol' • ¿.........................................................................................................8
n\(pM)\ 461 ~ ~................................................................................................................8
3.04140932*106—..............................................................................................................8
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11. The National Highway Traffic Safety Administration
(NHTSA) conducted an investigation to find out whether drivers
in the United States are wearing their seat belts (Associated Press,
August 25, 2003). The sample data were as follows.
Drivers who wear seat belts
Region Yeah No
Northeast 148 52
Mid West 162 54
South 296 74
West 252 48
------ -----
Total 858 228
b. A year earlier, the probability in the United States that a
driver was wearing a seat belt was 0.75. NHTSA Director Dr.
t What is the probability that a driver in the
o United States is wearing a seat belt?
Jeffrey Runge expected the probability to reach 0.78 in 2003.
Will you be satisfied with the results of the 2003 study?
c. What is the probability that seat belts are
used in different regions of the country? In
which region is the seat belt used the most?
__________ or
d. In the sample, what proportion of the drivers came from each
region of the country? In which region were the most drivers
selected? Which region comes second?
e. If you admit that in all regions the number of drivers is the
same, do you see any reason why the estimated probability in the
subsection a is so high?
Explain.
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12. In the United States there is a lottery that is played twice a week
in 28 states, the Virgin Islands and the District of Columbia. To play,
you must buy a ticket and select five numbers from 1 to 55 and one
number from 1 to 42. To determine the winner, 5 white balls are
drawn from 55 white balls and one red ball from 42 red balls.
Whoever matches the five white ball numbers and the red ball
number is the winner. Eight workers from a company hold the
record for the biggest prize, they won $365 million by matching the
numbers 15-17-43 44-49 of the white balls and 29 of the red balls. In
each game there are also other prizes. For example, whoever
matches all five numbers on the white balls wins a prize of $200,000
( www.powerball.com , March 19, 2006).
a. In how many ways can the first five numbers be selected?
b. What is the probability of winning the $200,000 by hitting the
five white ball numbers?
c. What is the probability of matching all the numbers and winning
the jackpot?
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