Table of Probability of Successful Donation Given DT and RT: P(D|DT,RT)

Each person has a blood type (O-,O+,A-,A+,B-,B+,AB-,AB+). The table above shows the probability of a successful blood transfusion given the donor's blood type (DT) and the receiver's blood type (RT). A "1" in this table means that the blood transfusion from DT to RT would be successful. Conversely, a "0" means that a transfusion from DT to RT would be unsuccessful, meaning that the receiver would die if such a transfusion took place. As you can see, O- donors can give to anyone. Conversely, AB+ receivers can receive blood from anyone.

P(DT) is the probability that a randomly selected donor would have a particular blood type. Likewise, P(RT) is the probability that a randomly selected receiver would have a particular blood type.

(a) What is the probability that a randomly selected donor and receiver would have a successful blood transfusion? (The answer is NOT 27/64)

(b) Suppose someone with an unknown blood type needs a transfusion. While their blood type is unknown, we do know that they underwent a successful blood transfusion from an O+ donor in the past. We have obtained an A- donor. What is the probability that the transfusion would be successful from this donor? (The answer is NOT 25% or 50%)

Most restaurants offer free refills for its customers who purchase a fountain soft drink. A certain buffet restaurant currently doesn’t. But, it has been argued that customers who drink more soft drinks tend to eat less and, thus, cost the restaurant less for the meal the customer eats. To test this argument, this restaurant offered free refills to a sample of 6 of its customers. The total number of glasses each customer drank, X, and the $ cost of the meal each ate, Y, were recorded. The findings along with some additional calculations appear in the following table.

Customer x y

1 2 10 - 0.5 2 0.25 4 - 1.0

2 1 8 - 1.5 0 2.25 0 0.0

3 3 6 0.5 - 2 0.25 4 - 1.0

4 0 13 - 2.5 5 6.25 25 - 12.5

5 4 6 1.5 - 2 2.25 4 - 3.0

6 5 5 2.5 - 3 6.25 9 - 7.5

15 48 0 0 17.50 46 - 25.0

Using the above results, determine the following. (Show your work and highlight your final answers either with a highlighter or by placing a box around it. Calculate all values to 4 decimal places.) DO NOT ANSWER THE FOLLOWING PARTS BY RUNNING EXCEL’S ‘Regression’ ANALYIS TOOL.

1. The standard deviation of Y

2. The standard deviation of X

3. The correlation coefficient between X and Y

4. The slope of the regression line expressing the linear relationship between cost and number of glasses

5. The y-intercept of this regression line

6. R²

Using any of your above answers and the value of SE(b₁) = .38333, at the .05 level of significance is there sufficient evidence that the more glasses of a soft drink the customer drink, the less the total cost of the meal that a customer consumes.? When answering this question, complete the following but DO NOT ANSWER ANY OF THESE PARTS BY RUNNING EXCEL’S ‘Regression’ ANALYIS TOOL. No diagrams are necessary but may be useful in determining correct answers.

Hypotheses

Test statistic

Decision rule in terms of the value of the test statistic

p-value (use the t-table, do not use Excel, in determining the p-value)

conclusion

can you put this in your own words?

Our class was divided into three groups and everyone followed the same procedure and steps. Each group had to keep track of their daphnia’s rate of growth based on how many lives and reproduce and how many die. To start off with this experiment, we had to come up a group name and then filled the “Daphnia life history data sheet” on which we recorded all our group member’s phone numbers and the date each person was responsible for collecting the information. We had total of seven 50 ml of plastic tube and we had them all labeled with our group name and the density of Daphnia. The tubes were labeled as follows: two tubes -1 D. magna per 2.0 ml of water, one tube – 1 D. magna per 1.0 ml of water and one tube of 1 D. magna per 0.5 ml of water. After that, we filled all of the tubes with 6 to 8 ml of well water that was in a big container. Throughout this whole experiment we used well water whenever we had to add water to the tubes. Then, our instructor provided us with three-day old Daphnia and after that we added Daphnia to the assigned tubes which are as followed: we added 5 Daphnia to tube labeled 1 D. magna per 2.0 ml of water and tube labeled 1 D. magna 1.0 ml of water received 5 daphnia each. Then these three-day old daphnia were obtained by placing egg in well water and collecting all the offspring that appeared during the next 24 hours. Then, we separated the adults form the babies and transfer the number of baby daphnia from their nursey to tube with a clean plastic dropper. We had to be really carefully when making the transfer so we don’t injure the daphnia. be careful to ensure that the tip of the dropper in submerged in the water before releasing the daphnia into your tubes. air bubbles can get trapped under the daphnia's carapace if you allow them to be exposed to the air. the, adjust the volume of water in each tube to 10 ml by adding or removing sufficient water with a dropper.

2. Determine the equilibium concentration of each of the reactants and products in Solution B-1 using the table provided below (ICE table). Fill in all blank values

3.Determine the equilibium concentration of each of the reactants and products in Solution B-2 using the table provided below (ICE table). Fill in all blank values

4.Determine the equilibium concentration of each of the reactants and products in Solution B-3 using the table provided below (ICE table). Fill in all blank values

5. Determine the equilibium concentration of each of the reactants and products in Solution B-4 using the table provided below (ICE table). Fill in all blank values

6.Determine the equilibium concentration of each of the reactants and products in Solution B-5 using the table provided below (ICE table). Fill in all blank values

I have no idea how to do problems 2-6. Could someone please help me. Your help is always greatly appreciated! Thank you in advance.

Foam Products, Inc., makes foam seat cushions for the automotive and aerospace industries. The company’s activity-based costing system has four activity cost pools, which are listed below along with their activity measures and activity rates:

The company just completed a single order from Interstate Trucking for 2,000 custom seat cushions. The order was produced in four batches. Each seat cushion required 0.3 direct labor-hours. The selling price was $141.20 per unit, the direct materials cost was $107 per unit, and the direct labor cost was $14.20 per unit. This was Interstate Trucking’s only order during the year.

Required:

Calculate the customer margin on sales to Interstate Trucking for the year.

F.J. Brewerton Retailers, Inc., must decide whether to build a small or a large facility at a new location in Omaha. Demand at the location will either be low or high, with probabilities 0.4 and 0.6, respectively. If Brewerton builds a small facility and demand proves to be high, he then has the option of expanding the facility. If a small facility is built and demand proves to be high, and then the reatiler expands the facitliy, the payoff is $270,000. If a small facility is built and demand proves to be high, but Brewerton then decides not to expand the facility, the payoff is $223,000.

If a small facility is built and demand proves to be low, then there is not option to expand and the payoff is $200,000. If a large facility is built and demand proves to be low, Brewerton then has the option of stimulating demand through local advertising. If he does not exercise this option, then the payoff is $40,000. If he does exercise the advertising option, then the response to advertising will either be modest or sizable, with probabilities of 0.3 and 0.7 respectively. If the response is modest, the payoff is $20,000. If it is sizable, the payoff is $220,000. Finally, if a large facility is built and demand proves to be high, then no advertising is needed and the payoff is $800,000.

a.) What should Brewerton do to maximize his expected payoff?

b.) What is the value of this expected payoff?

Greta has risk aversion of A = 3 when applied to return on wealth over a one-year horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of one-year strategies. (All rates are annual and continuously compounded.) The S&P 500 risk premium is estimated at 9% per year, with a standard deviation of 23%. The hedge fund risk premium is estimated at 11% with a standard deviation of 38%. The returns on both of these portfolios in any particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.

a-1. Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

a-2. What is the expected return on the portfolio? (Do not round intermediate calculations. Enter your answers as a decimal rounded to 4 places.)

Use the information in the chart to answer the questions that follow

Given the above information on two investments A and B, calculate the following statistics:

1. Calculate the Expected Return for A. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

2. Calculate the standard deviation for A. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

3. Calculate the Expected Return for B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

4. Calculate the standard deviation for B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

5. Assume that the expected return for A is 10% and the expected return for B is 5.5%. Calculate the expected return on a portfolio consisting of 60% A and 40% B. Give your answer in decimal form to 3 decimals places. For example, 9% is 0.09.

Find

-A continuous r.v. X follows uniform distribution , that is ? ~ ???????(?=0,?=1), Find the following probability
(a) P(0 < X < 0.3)
(b) P(0.5 < X < 1)
(c) Find the mean and variance of X

- A continuous r.v. X follows the pdf: ?(?)= 2?3, 1≤?≤2.
(a) Find the cdf of X for 1≤?≤2.
(b) Find the mean and variance of X.
(c) Find P(X = 1.22)

-Suppose that in a particular traffic environment, the distribution of time headway has the following form.
?(?)={??−2? ?≥00 ?<0
Determine the value of k for which f(x) is a valid pdf.

- The cdf of a r.v. X is given by:
?(?)={1−?−0.5? ?≥00 ?<0
Find the pdf of X

- An engineer designs a new battery to be used in a handheld calculator. The lifetime of the battery is exponentially distributed and has and expected lifetime of μ = 4000 hours.
(a). Given that the expected lifetime is μ = 4000 hours, what is the value of λ?
(b). What is the probability that the lifetime of the battery is less than 5000 hours? Clearly specify the probability statement!!
(c). What is the probability that the lifetime of the battery is exactly 2000 hours?

The stock of Jones Trucking is expected to return 15 percent annually with a standard deviation of 7 percent. The stock of Bush Steel Mills is expected to return 19 percent annually with a standard deviation of 10 percent. The correlation between the returns from the two securities has been estimated to be +0.3. The beta of the Jones stock is 1.2, and the beta of the Bush stock is 1.5. The risk-free rate of return is expected to be 6 percent, and the expected return on the market portfolio is 14 percent. The current dividend for Jones is $4. The current dividend for Bush is $6.