Decision under uncertainty

Zed and Adrian and run a small bicycle shop called"Z to A Bicycles". They must order bicycles for the coming month. Orders for the bicycles must be placed in quantities of twenty (20). If Zed and Adrian run out of bicycles during the month, then they will suffer a loss of "goodwill" among their customers. Zed and Adrian estimate that the demand for bicycles this month will be 10, 30, 50, or 70 bicycles but the probabilities for these possibilities are unknown. The table below depicts the profit that results from each possibility.

a.) Determine the best strategy using the maximin criterion. Show work that supports your answer.

b.) Determine the best strategy using the maximax criterion. Show work that sup- ports your answer.

c.) Determine the best strategy using the minimax regret criterion. Show work that supports your answer.

d.) Represent the payoff table in decision tree form.

A stock price is currently $100. Over each of the next two three-month periods it is expected to go up by 8% or down by 7%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $95?

Given are five observations collected in a regression study on two variables.

(a)

Develop the estimated regression equation for these data.

ŷ =

Use the estimated regression equation to predict the value of y when

x = 20.

Bond A is a 15 year, 9% semiannual-pay bond priced with a yield of maturity of 8%, while bond B is a 15 year, 7% semiannual-pay bond priced with the same yield to maturity. Given that both bonds have par values of $1,000, what would be the prices of these two bonds?

ABC Corporation issued $600,000 of 7% bonds due in 10 years. The bonds pay interest each July 1 and January 1. Assume an effective interest rate of 8%. Determine the price of the bond and prepare an amortization schedule for two years. What is the interest expense for January 1, 2021

A small town gets its water supply from three nearby lakes, A, B, and C. Sometimes in the late summer

the water level in a lake falls below a certain critical level. When this occurs, there is a risk that the water

from that lake will become polluted with E-Coli. If the water supply to the town becomes polluted, the

residents are advised to boil their water. If only the water level at lake A falls below the critical level,

experience has shown that the residents will have a 5% chance of a boil water advisory. Similarly, if

only the water levels at lakes B or C fall below the critical level, chances of a boil water advisory are

4% and 7%, respectively. If two or more lakes fall below the critical levels simultaneously, the risk

of a boil water advisory rises to 40%. Lake A falls below the critical level in 30% of the summers,

while this number is 50% and 20% for lakes B and C, respectively. The probability that exactly two

lakes will fall below their critical levels simultaneously is 12%, and it is equally likely to be any two of

the three. Finally, there is a 3% chance that all three lakes will simultaneously fall below their critical

levels. During some summer in the future:

a) What is the probability that the residents will have a boil water advisory? (answer:0.0914)

b) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical level at lake B alone? (answer:0.1707)

c) If the residents have a boil water advisory, what is the probability that the water level will fall

below the critical levels at two or more lakes simultaneously? (answer:0.6565)

You are dealt a hand of five cards from a standard deck of 52 playing cards. Calculate the probability of the given type of hand. (None of them is a recognized poker hand.)

1. Double royal interracial wedding: Two kings of one color, two queens of the other color, and a last non-royal card (neither king, queen, jack or ace).

Solve using a formula.

Examples:  C(5,3)C(33,3)/C(14,2) or C(5,3)C(33,3)C(4,1)/C(100,100)

Think of a technology that, in your opinion, clearly affects the workplace. Try to think of a technology that is not so common. (You might also think about the technology you wish to look into for the research paper.)
Create a dialogue / conversation between two people of approximately 100 lines - about two pages. In it, one person must “act” as if the technology has little or no impact on the workplace. The other (you, perhaps) must convince the first of its impact. That last person needs to provide examples of the unanticipated and anticipated consequences of the technology. Provide an

7. A psychologist is interested in determining whether immediate memory capacity is affected by sleep loss. Immediate memory is defined as the amount of material that can be remembered immediately after it has been presented. Twelve students are randomly selected from lower division college courses and randomly assigned to two groups of 6 each. One of the groups is sleep deprived for 24 hours before the material is presented. All subjects in the other group receive the normal amount of sleep (7-8 hours). The material consists of a series of slides, with each slide containing nine numbers. Each slide is presented for a short time interval (50 milliseconds), after which the subject must recall as many numbers as possible. On the following page are the results. The scores represent the percentage correctly recalled. Normal Sleep Group: 68 73 72 65 70 73 Sleep Deprived Group: 70 62 68 63 69 60

a. Describe (1) the independent variable and its levels, and (2) the dependent variable and its scale of measurement. Independent Variable- immediate memory capacity is affect by sleep Dependent- Variable- Scores represent the percentage correctly recalled between two groups b. Describe the null and alternative hypotheses for the study described. c. Using Excel, conduct a statistical test of the null hypothesis at p = .05. Be sure to properly state your statistical conclusion. d. Provide an interpretation of your statistical conclusion in part C. e. What type of statistical error might you have made in part C? f. Obtain the 95% confidence interval using the obtained statistic. g. Provide an interpretation of the confidence interval obtained in part f. h. Does the confidence interval obtained support your statistical conclusion? Explain your answer.

suppose that you are tossing two six sided dice one by one. What is the probability that (a) you will observe a total of 10? (b) You will observe a six on any dice? (c) You will observe a total at most of 7? (d) You will observe at least 11?