Consider three classes, each consisting of 20 students. From this group of 60 students, a group of 3 students is to be chosen. i. What is the probability that all 3 students are in the same class? [3 marks] ii. What is the probability that 2 of the 3 students are in the same class and the other student is in a different class? [3 marks] (b) In a new casino game, two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls to see if you will win any money. Suppose that you win $2 for each black ball selected, you lose $1 for each white ball selected, and you get nothing for each orange ball selected. If the casino lets you play this new casino game with no entry fee, what is the probability that you will not lose any money? [7 marks]

(c) A survey was conducted on lawyers at two different law firms about their annual incomes. The following table displays data for the 275 lawyers who responded to the survey. Annual Income Law Firm 1 Law Firm 2 Total Under $45,000 30 20 50 $45,000 to $89,999 35 40 75 $90,000 and over 100 50 150 TOTAL 165 110 275 Suppose we choose a random lawyer who responded to the survey. Are the events ”income is under $45,000” and ”employed at Law Firm 2” independent? [4 marks] (d) A smartphone company receives shipments of smartphones from three factories, labelled, 1, 2 and 3. Twenty-five percent of shipments come from factory 1 whose shipments contain 8% defective smartphones. Sixty-five percent of the shipments come from factory 2 whose shipments contain 6% defective smartphones. The remainder of the shipments comes from factory 3 whose shipments contain 4% smartphones. The company receives a shipment, but does not know the source. A random sample of 15 smartphones is inspected, and three of the smartphones are found to be defective. What is the probability that this shipment came from factory 2?

1.Test the hypothesis that the proportion of students who have the Wuhan flu is .3. Use a .10 significance level, a two-tail test and the following data: A sample of 100 students has 40 with the virus.

2 Test the hypothesis that the mean number of hours the Wuhan flu can live on a cell phone is more than 20. Use a .01 significance level and a one tail test and the following data: a sample of 50 phones has a sample mean =21.5 and a variance=9.

3 Test the null hypothesis that the proportion of students who believe TRUMP policy is appropriate dealing with the TRUMP virus is .6. The alternative hypothesis is the proportion >.6. Use a .05 significance level. A sample of 25 students has 19 think TRUMP policy is effective.

4) Are students avoiding events that average more than 20 people? A sample of 25 event has an average attendance of 23.3 people and a variance of 4 people. Use a significance level of 5% and a one-tail test.

5. Is the vaccine effective for the Wuhan flu? A sample of 30 students were given the vaccine and 12 got the virus. Without the vaccine, the rate of infection is 50%. Use a 1 tail test and a 5% significance level. What is the p value. [Khan academy has a good discussion of the P value]

6. Do students spend more than 6 ours a day on the phones? A sample of 150 students has an average usage of 8 hours and a variance of 6 hours. Use a 10% significance level.

Many people assume that when employers economize on safety programs the money they save improves profits, but that’s not the case. For one thing, poor safety practices raise wage rates, because wage rates are higher on jobs with riskier working conditions, other things equal. And poor safety and the injuries and illnesses it begets actually drive up costs, including medical expenses, workers’ compensation, and lost productivity. Consider the evidence. One study found a 9.4% drop in injury claims and a 26% average savings on workers’ compensation costs over 4 years in companies inspected by California’s occupational safety and health agency. A survey of chief financial officers concluded that for every one dollar invested in injury prevention, the employer earns two dollars; 40% said “productivity” was the top benefit of effective workplace safety. One forest products company saved over $1 million over 5 years by investing only about $50,000 in safety improvements and employee training. In the United States, work-related hearing loss costs employers about $242 million a year in workers’ compensation claims alone, costs that are probably avoidable through earmuffs, earplugs, and training. So one of the easiest ways to cut costs and boost profits is to spend money improving safety.

Assuming this is true, why do so many employers apparently cut corners on safety?

You're on a highly-classified project to design rockets of incredible speeds. There are two situations, one is a two-stage rocket and one is a three-stage rocket.

The two-stage rocket reaches a speed of .5c in relation to the launch-pad in deep space. In relation to the first stage, the second stage reaches a speed of .5c.

Each stage in the three-stage rocket reaches a speed of (1/3)c in relation to the launch-pad or in relation to the stage it separated from.

Calculate the final speeds of the last stages, and determine which rocket has the highest final speed. (c = speed of light)

1.) Use the definitions given in the text to find both the odds for and the odds against the following event.

-Flipping 4 fair coins and getting 0 heads.

The odds for getting 0 heads are what to what.​(Type a whole​ number.)

The odds against getting 0 heads are what to what. (Type a whole number)

2.) Determine whether the following individual events are overlapping or​ non-overlapping. Then find the probability of the combined event.

Getting a sum of either 4 or 8 on a roll of two dice

Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.

3.)Determine the probability of having 2 girls and 3 boys in a 5​-child family assuming boys and girls are equally likely.  

The probability of having 2 girls and boy sis is?

4.) Use the​ "at least​ once" rule to find the probabilities of the following event.

Getting at least one head when tossing seven fair coins

1. What different ways could we look at costs and conceptualize costs as they relate to a firm?
2. Why do costs matter to your firm? How can we employ an understanding of costs to optimally manage our firm?
3. You are the manager of a firm producing computers. How do you decide how many computers to produce for sale? Use a fully labeled economic model and a brief explanation to justify your thinking.
4. Two scenarios. First, you purchased a ticket to go to a concert for $20. When you arrive at the venue, you realize you lost your ticket. Would you purchase another one? Second, you are going to a concert that costs $20 and didn’t purchase a ticket. When you arrive at the venue, you realize you lost $20. Would you still purchase the ticket? Discuss and explain

Janice Huffman has decided to start Rundle Cleaning, a residential housecleaning service company. She is able to rent cleaning equipment at a cost of $710 per month. Labor costs are expected to be $50 per house cleaned and supplies are expected to cost $7 per house.

Required

a.Determine the total expected cost of equipment rental and the average expected cost of equipment rental per house cleaned, assuming that Rundle Cleaning cleans 20, 30, or 40 houses during one month. Is the cost of equipment a fixed or a variable cost?

b.Determine the total expected cost of labor and the average expected cost of labor per house cleaned, assuming that Rundle Cleaning cleans 20, 30, or 40 houses during one month. Is the cost of labor a fixed or a variable cost?

c.Determine the total expected cost of supplies and the average expected cost of supplies per house cleaned, assuming that Rundle Cleaning cleans 20, 30, or 40 houses during one month. Is the cost of supplies a fixed or a variable cost?

d.Determine the total expected cost of cleaning houses, assuming that Rundle Cleaning cleans 20, 30, or 40 houses during one month.

e.Determine the average expected cost per house, assuming that Rundle Cleaning cleans 20, 30, or 40 houses during one month.

Freedom Airlines recently started operations in the Southwest. The airline owns two airplanes, one based in Phoenix and the other in Denver. Each airplane has a coach section with 140 seats available. Each afternoon, the Phoenix based airplane flies to San Francisco with stopovers in Las Vegas and in San Diego. The Denver-based airplane also flies to San Francisco with stopovers in Las Vegas and in San Diego. Each airplane returns to its home-base with no stopovers.

Freedom Airlines uses two coach-fare classes: A discount fare (A) and a full fare (B). Discount fares are available with a 21-day advance purchase. Full fares applied at any time, up to the time of the flight.

Below is the daily fare and demand data for 16 selected Freedom Airline itineraries. Itineraries 1 through 6 apply to the Phoenix based airplane (leg 1); itineraries 7 through 12 apply to the Denver based airplane (leg 2); itineraries 13 and 14 apply to the Phoenix based airplane (leg 3); itineraries 15 and 16 apply to the Denver based airplane (leg 4):

1. Develop a revenue management (maximizing) model based on the information given in the scenario.
2. How many seats should be allocated to each of the 16 itineraries to maximize revenue?
3. What is the (maximum) expected revenue to be earned per day for all 16 flights?
4. Assume operating costs for each of the legs is as follows:
5. Leg 1 = $20,250
6. Leg 2 = $19,750
7. Leg 3 = $20,500
8. Leg 4 = $19,500

What is the expected operating income for each of the legs? And in total for Freedom Airlines, given these 16 itineraries?

1. Develop a revenue management (maximizing) model based on the information given in the scenario.
2. How many seats should be allocated to each of the 16 itineraries to maximize revenue?
3. What is the (maximum) expected revenue to be earned per day for all 16 flights?
4. Assume operating costs for each of the legs is as follows:
   1. Leg 1 = $20,250
   2. Leg 2 = $19,750
   3. Leg 3 = $20,500
   4. Leg 4 = $19,500

What is the expected operating income for each of the legs? And in total for Freedom Airlines, given these 16 itineraries?

The personnel director for a small manufacturing company has collected the data found in the table 1 describing the salary (Y) earned by each machinist in the factory along with the average performance rating (X₁) over the past 3 years, the years of service (X₂), and the number of different machines each employee is certified to operate (X₃).

The personnel director wants to build a regression model to estimate the average salary an employee should expect to receive based on his or her performance, years of service, and certifications.

a. Prepare three scatter plots showing the relationship between the salaries and each of the independent variables. What sort of relationship does each plot suggest?

b. If the personnel director wanted to build a regression model using only one independent variable to predict the salaries, what variable should be used?

c. If the personnel director wanted to build a regression model using only two independent variables to predict the salaries, what two variables should be used?

d. Compare the adjusted-R² statistics obtained in parts b and c with that of a regression model using all three independent variables. Which model would you recommend that the personnel director use?

e. Suppose the personnel director chooses to use the regression function with all three independent variables. What is the estimated regression function?

f. Suppose the company considers an employee’s salary to be “fair” if it is within 1.5 standard errors of the value estimated by the regression function in part e. What salary range would be appropriate for an employee with 12 years of service, who has received average reviews of 4.5, and is certified to operate 4 pieces of machinery?

The firm is financed by 40% of debt and 60% of equity. It has the weigthed average cost of capital of 15%. The cost of equity is 25%. What is the cost of debt? Assume that there are no taxes.And think about another situation. The firm is financed by 40% of debt and 60% of equity. It has the weigthed average cost of capital of 15%. The cost of debt is 8%. What is the cost of equity? Assume that there are no taxes.Please answer the questions with two parts.