A transportation app developer knows that the commute times for a specific route follow an approximately normal distribution with a mean of 30 minutes and a standard deviation of 6 minutes. Using the norm.dist() function in excel, the developer has calculated the following probabilities for specific commute times. Probability Calculations P (Commute < 16.04) = 0.01 P (Commute < 20) = 0.048 P (Commute < 20.13) = 0.05 P (Commute < 25) = 0.202 P (Commute < 35) = 0.798 P (Commute < 39.87) = 0.95 P (Commute < 40) = 0.952 P (Commute < 43.96) = 0.99 9. What is the probability that a commute is between 25 and 40 minutes? 10. Name the two values (don’t round), equidistant from the mean of 30 minutes, such that 90% of all commute times are between these values?

Answers

Answer 1

9.  Probability (between 25 and 40 minutes) = 0.75.

10. Two values are 18.3 minutes (lower value), and 41.7 minutes (upper value)

For the probability that a commute is between 25 and 40 minutes, calculate the difference between the cumulative probabilities of the upper and lower bounds.

P(25 < Commute < 40) = P(Commute < 40) - P(Commute < 25)

Using the given probability values:

P(25 < Commute < 40) = 0.952 - 0.202

P(25 < Commute < 40) = 0.75

Therefore, the probability that a commute is between 25 and 40 minutes is 0.75.

10. To find the two values equidistant from the mean of 30 minutes such that 90% of all commute times are between these values, calculate the corresponding z-scores.

Since the data follows an approximately normal distribution, use the z-score formula:

z = (x - μ) / σ

Where:

z is the z-score

x is the value

μ is the mean

σ is the standard deviation

To find the z-scores corresponding to the cumulative probabilities, use the norm.inv() function in Excel.

The z-score for the lower value, which corresponds to the 5th percentile (0.05 cumulative probability), is given by:

z1 = norm.inv(0.05, 0, 1)

The z-score for the upper value, which corresponds to the 95th percentile (0.95 cumulative probability), is given by:

z2 = norm.inv(0.95, 0, 1)

Now, find the corresponding commute times by rearranging the z-score formula:

x = z * σ + μ

Using the given mean (μ = 30) and standard deviation (σ = 6):

For the lower value:

x1 = z1 * σ + μ

For the upper value:

x2 = z2 * σ + μ

Calculating the values:

For the lower value:

x1 = norm.inv(0.05, 30, 6) ≈ 18.3 minutes

For the upper value:

x2 = norm.inv(0.95, 30, 6) ≈ 41.7 minutes

Therefore, the two values (without rounding) equidistant from the mean such that 90% of all commute times are between them are 18.3 minutes & 41.7 minutes

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Related Questions

what is the role of one main aggregate in the economy?​

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The Gross Domestic Product (GDP), which counts the value of all goods and services generated in a nation, plays a key aggregate function in the economy.

Economic aggregates are measurements of the total economic activity within a nation-state or a geographic area. Aggregate supply is the entire amount of products and services produced within an economy at a specific level of overall price over a specific time frame.

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As a result, the significance of the role of one main aggregate in the economy are the aforementioned.

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explain in a essay on good or bad services that you have at a hospital​

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Title: An Assessment of Good and Bad Services in a Hospital

Hospitals are crucial institutions that provide essential medical care to individuals during times of illness or injury.

The quality of services offered by hospitals plays a significant role in patient satisfaction, outcomes, and overall healthcare experience.

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In the present quickly developing medical services, administration quality assumes a vital part in forming patients' encounters and fulfillment. Hospitals, as the essential suppliers of medical services administrations, are supposed to convey great consideration in a humane and effective way.

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The CEO is interested in learning more about probability and how it works. The CEO is also asking about how probability and analytics can be integrated into the business model. In the process of looking for information on probability, you find that it is important to understand optimization and forecasting and how they can be applied to benefit the business. Do some research and present the results for the CEO. The following is the necessary information to complete this lab assignment. Deliverables Step 2: Probability Research • Considering the CEO's request, you determine that some research needs to take place. • Define the following terms for the CEO and locate some chart examples of each type of analysis. o Probability o Optimization o Forecasting Step 3: Integrating Data Research for Business • In one to two paragraphs, discuss what role probability and statistics play in business decisions. • In one to two paragraphs, discuss any ethical considerations when doing probability. • Summarize by explaining why probability is a good method for the CEO to consider.

Answers

Step 2: Probability Research Probability, Optimization, Forecasting.

Step 3: Integrating Data Research for Business.

Probability:

Probability is a branch of mathematics that deals with the likelihood of events occurring. It is a measure of uncertainty and is expressed as a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

Optimization:

Optimization involves finding the best possible solution from a set of alternatives. It aims to maximize desired outcomes or minimize undesirable ones, considering constraints and objectives.

Forecasting:

Forecasting is the process of predicting future events or outcomes based on historical data and statistical models. It helps businesses anticipate demand patterns, market trends, and other factors that can influence decision-making.

Step 3: Integrating Data Research for Business

Probability and statistics play a crucial role in business decisions. They provide a framework for analyzing and interpreting data, assessing risks, making predictions, and supporting evidence-based decision-making.

When working with probability, ethical considerations are important. It is essential to ensure that data used in probability analysis is collected ethically, respects privacy and confidentiality, and adheres to relevant legal and regulatory requirements.

Probability is a valuable method for the CEO to consider because it provides a systematic and quantitative approach to analyzing uncertainty and making informed decisions.

By integrating probability into the business model, the CEO can better understand risks, optimize resource allocation, improve forecasting accuracy, and ultimately enhance strategic decision-making and business performance.

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57. Mark Green is considering buying a new Honda Accord. The purchase price of the car is $21,000 but Mark has a trade-in worth $4500. Mark needs a loan to buy the car and knows that his local bank requires him to put down 10% of the purchase price after the value of the trade-in is considered. Mark also knows that bank will charge 8% for the loan and require monthly payments over the next 4 years. What is the size of Mark‟s monthly payments if he makes the minimum down payment on the car?

Answers

Note that , Mark's monthly payments will be approximately $335.89 if he makes the minimum down payment on the car.

How is this so?

Given

Loan amount - $14,850

Loan term - 48 months

Interest rate - 0.0067 per month(8   % annual rate divided by 12 months)

Using the formula for a fixed- rate loan,the monthly   payment (P) can be calculated as follows:

P =   (Loan Amount * Monthly Interest Rate) /(1 - (1 + Monthly Interest Rate)^(-Number of Months))

P = ($  14,850 * 0.0067) /(1 - (1 + 0.0067)^(-48))

computing we have

P = ($99.50) / (1 - (1.0067)^(-48))

P = ($99.50) / (1 - 0.7035)

P = ($99.50) / (0.2965)

P ≈ $335.89

Therefore, Mark's monthly payments will be approximately $335.89 if he makes the minimum down payment on the car.

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What are some consideration the company and Hr shpula be aware of making changes​

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There are some considerations the company and HR should be aware of when making changes related to this case study is:

Employee well-being.Training and upskilling.Communication.

Employee welfare: HR should make sure that workers are aware of the changes and are aware of how they will affect them.

Training and upskilling: To aid employees in adjusting to the changes, HR should design processes for upskilling and deskilling.

Communication: HR should make it easier for employees to understand the changes, including why they are being made, what results are anticipated, and how they will be implemented.

As a result, the significance of the considerations the company and HR should be aware of when making changes are the aforementioned.

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Your question is incomplete, but most probably the full question was.

What are some considerations the company and HR should be aware of when making changes related to this case study?

Savings plans A and B have both durations of 5 calendar years.
Savings plan A pays 5.7% annual interest, paid at the end of each year.
Savings plan B pays 5.4% annual interest, paid on monthly basis (12 times a year).
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Answers

Based solely on the interest earned, Savings Plan A would be preferred over Savings Plan B.

To determine which savings plan is preferred, we can compare the total interest earned under each plan over the 5-year duration.

For Savings Plan A, the annual interest rate is 5.7%, and the interest is paid at the end of each year. Therefore, the total interest earned can be calculated using the simple interest formula: Principal x Rate x Time. Assuming a principal of $1,000, the total interest earned would be $1,000 x 0.057 x 5 = $285.

For Savings Plan B, the annual interest rate is 5.4%, and the interest is paid on a monthly basis (12 times a year). This means that the interest is compounded monthly.

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Comparing the total interest earned, we can see that Savings Plan A yields a higher interest amount ($285) compared to Savings Plan B ($279.67).

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A white paper is a report or guide that ________ readers about a complex issue. It is meant to help readers understand an issue, solve a problem, or make a decision.

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A white paper is a report or guide that educates or informs readers about a complex issue.

What is a whitepaper?

It is meant to help readers understand the intricacies of a particular topic, provide insights, propose solutions, or aid in decision-making. White papers are typically authoritative and objective in nature, presenting in-depth information, analysis, and recommendations related to the subject matter.

They are commonly used in business, government, and academic contexts to address complex issues and provide valuable knowledge to the intended audience.

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A business from any three business sectors is industry. Businesses clearly differ in what they do.

Businesses are frequently classified according to their industry or sector. An industry is a group of businesses which are related in terms of their primary activity, such as car manufacturing or grocery sales. Smaller industries (such as car manufacturing) can be grouped to larger industry sectors (such as the manufacturing sector in general). An individual business is classified as belonging to a specific industry based on its primary activity.

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Select the best answer.
The location where hazmats are stored must be clearly marked, and a must be posted in that area
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Answers

Where hazmat are put away should be plainly checked, and a should be posted in that space are SDS. Subsequently choice (B) is right.

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The business environment is the set of internal and external factors that affect the operations and success of a business. It includes factors such as economic conditions, political and legal systems, technological advancements, social and cultural factors, and competitive forces.

Understanding the business environment is important for businesses because it enables them to identify opportunities and threats that may impact their operations.

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Similarly, a business operating in an unstable economic environment may need to adjust its pricing or marketing strategies to remain viable.

In summary, the business environment is a complex and dynamic system that affects businesses in various ways, and understanding it is critical for success in the business world.

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A long-term incentive is a type of
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A long-term incentive is a type of incentive given to employees that is designed to be paid over an extended period or longer term. It is typically used as a way to align the interests of employees with the long-term goals of the organization. Long-term incentives are often provided in addition to regular salary or short-term incentives and are commonly used for executive-level employees or key members of the organization.

In two to three sentences, answer the following:

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What information you can obtain from a stock quote?

Answers

The most important information needed to receive a stock quote is the ticker symbol of the specific stock.

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Additionally, some stock quotes may provide additional data such as the company's market capitalization, dividend yield, and earnings per share.

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What is meant by the concept entrepreneur?​

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Answer: An entrepreneur is someone who has an idea and who works to create a product or service that people will buy, as well as an organization to support that effort.

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Answers

Answer:

Small businesses can signal emerging trends and needs to large businesses

Note: Write your response with a complete sentence (to get the full marks) in the space provided; no attachments or email will be considered for marking.

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Answers

Point A represents inefficient use of resources and Point E represents efficienct use of resources. Any point lying on the PPF curve is an efficient use of resources and and any point lying inside the PPF such as Poni A is underutilization

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Answers

Here's an example of a WBS for the knowledge area of Human/Resource Management for a low-cost housing project:

The wbs for a knowledge area of Human/Resource Management for a low-cost housing project

Human/Resource Management

1.1 Staffing Plan

1.1.1 Define project roles and responsibilities

1.1.2 Identify required staffing resources

1.1.3 Determine the project team structure

1.1.4 Develop a staffing plan and budget

1.2 Recruitment and Selection

1.2.1 Create job descriptions and specifications

1.2.2 Advertise and promote job openings

1.2.3 Review resumes and conduct initial screenings

1.2.4 Conduct interviews and select candidates

1.2.5 Perform background checks and reference checks

1.2.6 Extend job offers and negotiate terms

1.3 Training and Development

1.3.1 Assess training needs for project team members

1.3.2 Develop a training plan and schedule

1.3.3 Conduct training sessions and workshops

1.3.4 Provide on-the-job training and mentoring

1.3.5 Evaluate training effectiveness and adjust as needed

1.4 Performance Management

1.4.1 Set performance expectations and goals

1.4.2 Monitor and assess individual and team performance

1.4.3 Provide feedback and coaching to improve performance

1.4.4 Conduct performance appraisals and evaluations

1.4.5 Identify and address performance issues or conflicts

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1.5.1 Identify project resource requirements

1.5.2 Allocate resources based on project needs

1.5.3 Monitor resource utilization and availability

1.5.4 Optimize resource allocation to meet project objectives

1.6 Stakeholder Management

1.6.1 Identify project stakeholders and their interests

1.6.2 Develop a stakeholder engagement plan

1.6.3 Communicate and manage stakeholder expectations

1.6.4 Address stakeholder concerns and resolve conflicts

1.6.5 Maintain positive relationships with stakeholders

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what is the difference between a checking agreement and a checking statement?

Answers

A checking account is an account that is used to keep track of a person's transactions. A checking agreement is an agreement between the bank and the account holder that outlines the terms of the account.

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A checking agreement is a contract between the bank and the account holder that outlines the terms of the account. This includes things like the minimum balance requirement, fees that may be charged, and the interest rate that will be paid on the account. The agreement also outlines the rights and responsibilities of the account holder and the bank. A checking statement is a document that is sent to the account holder by the bank that shows the activity that has occurred in the account over a certain period of time.

This includes things like deposits, withdrawals, and checks that have cleared. The statement also shows the current balance in the account. The statement is typically sent out on a monthly basis but can be requested more frequently if needed.

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write a 5 minute oral presentation about any three types of shares​

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Shares represent ownership in a company and provide investors with various rights and benefits.

In this oral presentation, explore three common types of shares: common shares, preferred shares, and treasury shares.

Common Shares: Common shares, also known as ordinary shares, are the most common type of shares held by investors. Owners of common shares have voting rights in the company's decision-making processes, such as electing the board of directors.Preferred Shares: Preferred shares are a type of equity that offers certain preferences over common shares. Preferred shareholders have a higher priority when it comes to receiving dividends.Treasury Shares: Treasury shares refer to shares that a company has repurchased from existing shareholders and holds in its own treasury. These shares are no longer considered outstanding and do not carry voting rights.

Thus, by comprehending these distinctions, investors can make informed decisions and navigate the complex world of stock ownership.

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I. A clinic encourages its customers to have their bond checked with the claim that one out
of four 60-year-old men need to be supplemented with glucosamine. If this is true, what is
the probability of the following events:
a. Two out of the next eight 60 year-old men need to be supplemented with glucosamine
b. Three out of the next 12 60 year-old men need to be supplemented with glucosamine

Answers

A clinic encourages its customers to have their bond checked with the claim that one out of four 60-year-old men need to be supplemented with glucosamine. If this is true, then the probability of the following events is Two out of the next eight 60 year old men need to be supplemented with glucosamine.

Glucosamine is a naturally occurring compound in the body. It is required for the formation and repair of cartilage as well as other body tissues.

Because glucosamine production slows in age, some people take glucosamine supplements to help them fight aging-related health issues like osteoarthritis. The majority of supplements are made from the shells of marine life, such as prawns and crabs.

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Search the Internet and locate a job that you would consider applying for.
Construct a Cover Letter for this actual job.
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Answers

A Cover Letter for this actual job.

[Your Name]

[Your Address]

[City, State, ZIP Code]

[Email Address]

[Phone Number]

[Today's Date]

[Recipient's Name]

[Company Name]

[Company Address]

[City, State, ZIP Code]

Dear [Recipient's Name],

I am writing to express my keen interest in the [Job Title] position at [Company Name], as advertised on [Job Board/Company Website]. With my strong background in [Relevant Skills/Experience], I am confident in my ability to contribute to the success of your organization.

Having [X years] of experience in [Industry/Field], I have honed my skills in [Key Skills/Expertise], which I believe align perfectly with the requirements of the [Job Title] role. I am particularly drawn to [Company Name]'s commitment to [Specific Company Values/Initiatives] and its reputation for excellence in [Industry/Field].

Throughout my career, I have demonstrated a strong track record in [Relevant Achievements/Projects], showcasing my ability to [Specific Skills/Results]. I am highly skilled in [Technical Skills/Software], and I possess excellent [Soft Skills/Abilities], allowing me to collaborate effectively with cross-functional teams and deliver outstanding results.

I am excited about the opportunity to contribute to [Company Name]'s ongoing success and would welcome the chance to discuss further how my skills and experience align with your organization's goals. Enclosed is my resume for your review.

Thank you for considering my application. I look forward to the possibility of meeting with you to discuss how my qualifications make me a strong fit for the [Job Title] position at [Company Name].

Sincerely,

[Your Name]

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