Show your work concisely. If you utilize Excel functions or online
calculators specify the function/calculator and ALL inputs. You may find the
reading on probability fundamentals useful in answering c) and d)
The daily return of a certain stock is normally distributed with a mean of
0.30% and a standard deviation of 2.50%.
a.
(already solved on the quiz) Find
the probability that the return on a randomly selected day is negative. Provide
a simple picture of the normal distribution and clearly label what the
probability found refers to.
b.
Find the level, L, such that
there is a 20% chance that the daily return on a randomly selected day exceeds
L. Provide a simple picture of the normal distribution and clearly label
the value found on the picture.
c.
Find the probability that the
return is negative on each of 4 randomly selected days.
Problem 2
(From Decision Making Under Uncertainty by David E. Bell and Arthur
Schleifer, Jr., Course Technology Inc.)
Sarah Chang, owner of a small electronics company, is considering
submitting a proposal for an electronic timing system for the 2008 Olympic
Games. The deadline for submitting a proposal is six months away. For several
years, Changs company has been developing a new microprocessor to create a new
timing system that would be superior to any product currently on the market.
However, progress in research and development has been slow, and Chang is
unsure about whether her staff can produce the microprocessor in time. Chang
estimates the chance that they will succeed in developing the microprocessor in
time to be 40%. If they succeed in developing the microprocessor, there is an
excellent chance that Changs company will win the $1 million Olympic contract.
Chang estimates this chance to be 90%.
Chang can also submit a proposal based on an alternative, inferior timing
system that has already been developed. She estimates the chance of winning the
contract with the existing system to be 5%. She is allowed to submit at most
one proposal.
If she pursues the new microprocessor, Chang must invest $200,000 in
further research and development. In addition, making a proposal requires
developing a prototype timing system at an additional cost of $50,000
(regardless of whether the technology used is new or old). Finally, if Chang
wins the contract, the finished product will cost an additional $150,000 to
produce (regardless of the technology).
a.
Draw (by hand) a decision
tree to model Changs decision. Include as Exhibit A(pasting a picture
from a smartphone or camera into MS Word is fine, or you can use any software
you want to lay out the structure).
o
Do not put any numbers
(probabilities, costs, etc.) on your drawing.
o
The tree should show the structure
and logic of the decision process.
o
Distinguishing
between decision and chance nodes, and naming the various nodes and
branches, is critical.
o
Create a tree that is as general
as possible do not eliminate certain branches from consideration because of
the specific values of the inputs as presented in the case.
o
Recall that the key to success is
determining what decision/event happens first, and then building out the tree
in sequential order.
b.
Implement your decision tree using PrecisionTree.
Include the full tree as Exhibit B.
o
Keep all the default settings in
the window titled PrecisionTree Model Settings except the tree name. You
can name your tree whatever you wish.
o
If you wish, you can create a single-page
printout of your tree as follows: Go to the Page Setup window by either
clicking on Office button/Print/Print Preview/Page Setup, or alternatively from
the Page Layout tab/Page Setup group. In the Page Setup window, select the Page
tab. Under the Scaling section, select Fit to 1 page wide by 1 page tall. A
Landscape orientation may give a better fit than a Portrait orientation.
c.
Using the Decision Analysis tools
of PrecisionTree, create the optimal tree. Include a figure of the optimal tree
as Exhibit C. Describe the optimal decision.
d.
Again using the Decision Analysis
tool, summarize the possible outcomes and their probabilities. What is the
probability that the project will return a profit?
Show your work concisely. If you utilize Excel functions or online
calculators specify the function/calculator and ALL inputs. You may find the
reading on probability fundamentals useful in answering c) and d)The daily return of a certain stock is normally distributed with a mean of
0.30% and a standard deviation of 2.50%.a.
(already solved on the quiz) Find
the probability that the return on a randomly selected day is negative. Provide
a simple picture of the normal distribution and clearly label what the
probability found refers to.b.
Find the level, L, such that
there is a 20% chance that the daily return on a randomly selected day exceeds
L. Provide a simple picture of the normal distribution and clearly label
the value found on the picture.c.
Find the probability that the
return is negative on each of 4 randomly selected days.Problem 2(From Decision Making Under Uncertainty by David E. Bell and Arthur
Schleifer, Jr., Course Technology Inc.)Sarah Chang, owner of a small electronics company, is considering
submitting a proposal for an electronic timing system for the 2008 Olympic
Games. The deadline for submitting a proposal is six months away. For several
years, Changs company has been developing a new microprocessor to create a new
timing system that would be superior to any product currently on the market.
However, progress in research and development has been slow, and Chang is
unsure about whether her staff can produce the microprocessor in time. Chang
estimates the chance that they will succeed in developing the microprocessor in
time to be 40%. If they succeed in developing the microprocessor, there is an
excellent chance that Changs company will win the $1 million Olympic contract.
Chang estimates this chance to be 90%.Chang can also submit a proposal based on an alternative, inferior timing
system that has already been developed. She estimates the chance of winning the
contract with the existing system to be 5%. She is allowed to submit at most
one proposal.If she pursues the new microprocessor, Chang must invest $200,000 in
further research and development. In addition, making a proposal requires
developing a prototype timing system at an additional cost of $50,000
(regardless of whether the technology used is new or old). Finally, if Chang
wins the contract, the finished product will cost an additional $150,000 to
produce (regardless of the technology).a.
Draw (by hand) a decision
tree to model Changs decision. Include as Exhibit A(pasting a picture
from a smartphone or camera into MS Word is fine, or you can use any software
you want to lay out the structure). o
Do not put any numbers
(probabilities, costs, etc.) on your drawing.o
The tree should show the structure
and logic of the decision process.o
Distinguishing
between decision and chance nodes, and naming the various nodes and
branches, is critical.o
Create a tree that is as general
as possible do not eliminate certain branches from consideration because of
the specific values of the inputs as presented in the case.o
Recall that the key to success is
determining what decision/event happens first, and then building out the tree
in sequential order.b.
Implement your decision tree using PrecisionTree.
Include the full tree as Exhibit B. o
Keep all the default settings in
the window titled PrecisionTree Model Settings except the tree name. You
can name your tree whatever you wish.o
If you wish, you can create a single-page
printout of your tree as follows: Go to the Page Setup window by either
clicking on Office button/Print/Print Preview/Page Setup, or alternatively from
the Page Layout tab/Page Setup group. In the Page Setup window, select the Page
tab. Under the Scaling section, select Fit to 1 page wide by 1 page tall. A
Landscape orientation may give a better fit than a Portrait orientation.c.
Using the Decision Analysis tools
of PrecisionTree, create the optimal tree. Include a figure of the optimal tree
as Exhibit C. Describe the optimal decision.d.
Again using the Decision Analysis
tool, summarize the possible outcomes and their probabilities. What is the
probability that the project will return a profit?