Bob Sparrow purchases steak from a local meatpacking house. The meat is purchased on Monday at $2.00 per pound, and the shop sells the steak for $3.00 per pound. Any steak left over at the end of the week is sold to a local zoo for $0.50 per pound. The possible demands for steak and the probability of each are shown in the following table:

Demand (lbs.) Probability

20 0.2

21 0.3

22 0.5

Bob must decide how much steak to order in a week. Bob wants to maximize expected value. What is his expected value when purchasing optimally? [Hint: construct a payoff table for each of his decisions and each state of nature.] A) 20 B) 20.5 C) 20.25 D) 21 9.

What is Bob Sparrow’s Expected Value of Perfect Information? A) 20.5 B) 1.3 C) 0.8 D) 1.05

Probability and Decision Analysis

A smartphone supplier in Sydney is considering three alternative investment options: a large store, a small store, or an outlet in the shopping mall.  

Profits from selling smartphones will be affected by the customer demand for smartphones in Sydney. The following payoff table shows the profit that could result from each investment, in dollars ($).  

1. What choice should be made by the optimistic decision maker?

2. What choice should be made by the pessimistic decision maker?

3. Compute the regrettable from the data.

4. What decision should be made under minimax regret approach?

5. What choice should be made under the expected value approach?

With excel

Using the data, fit an appropriate regression model to determine whether
time spent studying (hours) is a useful predictor of the chance of passing the exam (result, 0=fail 1=pass). Formally assess
the overall fit of the model.

DATA three;
INPUT result hours;
/* result=0 is fail; result=1 is pass */
cards;
0 0.8
0 1.6
0 1.4
1 2.3
1 1.4
1 3.2
0 0.3
1 1.7
0 1.8
1 2.7
0 0.6
0 1.1
1 2.1
1 2.8
1 3.4
1 3.6
0 1.7
1 0.9
1 2.2
1 3.1
0 1.4
1 1.9
0 0.4
0 1.6
1 2.5
1 3.2
1 1.7
1 1.9
0 2.2
0 1.3
1 1.5
;
run;

1. Your brother Eric plays hockey and you attend their game. Eric likes to be the goalkeeper, but it depends on who his coach is that day. Coach Peter prefers Eric to not be goalkeeper and will assign Eric to be a goalkeeper with 0.3 probability. Coach Jared will assign Eric to be a goalkeeper 50% of the time. Coach Jared is the main coach attending 8 out of 10 games. A.) Fill in the probability tree or tree diagram to display this scenario. B.) A food truck near the west coast sells the best tacos. 75% of the time, people will choose the tacos vs something else. The cooks need help calculating the chances of the following situations. What is the chance of selling none of the customers the tacos given there are 5 customers in line? Use 5 decimals. What is the probability of selling the tacos to at least one customer of the 5 in line? Use hand calculations and use 5 decimals.

Exercise 11-29 Cost Allocation: Step Method (LO 11-3) Caro Manufacturing has two production departments, Machining and Assembly, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of August follow: Proportion of Services Used by Department Direct Costs Maintenance Cafeteria Machining Assembly Machining $ 120,000 Assembly 80,000 Maintenance 53,000 — 0.2 0.5 0.3 Cafeteria 42,000 0.7 — 0.2 0.1 Required: Use the step method to allocate the service costs, using the following: a. The order of allocation starts with Maintenance. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.) b. The allocations are made in the reverse order (starting with Cafeteria). (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations.)

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+) or losses (−) in seconds per week.

Data File

a)State the null hypothesis and the alternate hypothesis. State the decision rule for 0.02 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

b)Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

c)Is it reasonable to conclude that the mean gain or loss in time for the watches is 0? Use the 0.02 significance level.

d)Estimate the p-value.

For a sample of 12 trees, the volume of lumber (in m³) and the diameter ( in cm ) at a fixed height above the ground level was measured. The results were as follows.

Use Excel sheet

a)Construct a scatterplot of volume ( y ) versus diameter ( x ). using Excel

b)Compute the least-square line for predicting volume from diameter.

c)Compute the fitted value and residual for each point. d)If two trees differ in diameter by 8 cm, by how much would you predict their volume to differ?

e)Predict the volume of a tree whose diameter is 44 cm.

f)For what diameter would you predict a volume of 1m³

1.

a. A researcher wishes to estimate the proportion of adults who have​ high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.3 with 99% confidence?

b.

it is believed that people prefer rubies over other gems. In a recent simple random survey of 150 people, 63 said they would prefer a ruby over other gems. Use this sample data to complete a hypothesis test to determine if a majority of people would prefer a ruby. over other gems at the 0.01 significance level.

Be sure to include all the steps for a complete hypothesis test - start and end in context, test conditions, show formulas and numbers used, clearly state REJECT or FAIL TO reject.

c.

If 12 jurors are randomly selected from a population that is 45% Hispanic, what is the probability that 2 or fewer jurors will be Hispanic?

In order to improve the financial Situation of Thoughts, the Manager looked into expansion plans and decided to offer caterings for events. For the catering business, the manager is offering his customers a selling price p that depends on demand, where p= 9 - 0.02*D.

a- Calculate the Quantity that Maximises Revenue.

b- Calculate the Quantity that Maximises Profit (Refer to problem 1 for costs).

Problem 1 Costs:

Rental $80 per day

Coffee beans $5 per Coffee Cup

Sugar $0.3 per Coffee Cup

Flavors $ 0.5 per Coffee Cup

Filtered water $0.2 per Coffee Cup

Labor $30 per day

c- Calculate the Breakeven point(s).

No Ready-to use Formula should be used in this Problem, show your iterations. Ready-to-use formulas and Calculator-derived results will NOT be accepted

A)

A student stretches an elastic band by 0.8 m in 0.5 seconds. The spring constant of the elastic band is 40 N/m. What was the power exerted by the student?

B)

A student pushes a 0.2 kg box against a spring causing the spring to compress 0.15 m. When the spring is released, it will launch the box vertically into the air. What is the maximum height the box will reach if the spring constant is 300 N/m?

C)

A student connects a 1 hp motor to a bicycle. How much time will it take for the bicycle to accelerate from rest to a speed of 5.0 m/s if the combined mass of the student and the bicycle is 120 kg? (1 hp = 746 W)