Review Full Anonymous No Quiz 7 80 Points Directions Show

Review Full Anonymous Noquiz 7 80 Pointsdirectionsshow Your W

Review: Full, Anonymous: No Quiz #7 / 80 points DIRECTIONS : Show your work to earn partial credit. 1. The management of a large insurance company believes that workers are more productive if they are happy with their jobs. To keep track of their 815 workers’ satisfaction, the company regularly conducts surveys. According to a recent survey, the mean job satisfaction score for all workers at this company was 13.25 (on a scale of 1 to 20) and the standard deviation was 1.6. Assume that the job satisfaction scores of workers are normally distributed. (56 points) a) What is the probability that a randomly selected worker will have a job satisfaction score between 14 and 18.5? Interpret the meaning of your answer. (16 points) b) A worker with a score of 9.0 or less is considered very unhappy with his/her job. Approximately how many workers are very unhappy with their jobs? (15 points) c) A worker with a score in the top 7% of scores is considered to be very happy with his/her job. What is the minimum score needed to be considered very happy? Round your answer to the nearest tenth. Which percentile have you just found? (15 points) d) A worker at this company with a score in the bottom 2.5% of scores is viewed as needing intensive job counseling with a job satisfaction score of ______ or less. Fill in the blank. Round to the nearest tenth.(10 points) 2. A television manufacturer is studying television remote control usage. One of the criteria they are measuring is the distance at which people attempt to activate the television set with the remote control. They have discovered that the activation distances are normally distributed with a mean distance of 6 feet and a standard deviation of 2.75 feet. If a remote’s maximum range is 10 feet, what percentage of the time will users attempts to operate the remote outside of its operating limit? (12 points) 3. Scores for a civil service exam are normally distributed, with a standard deviation of 6.9. To be eligible for civil service employment, you must score in the top 5%. If the lowest score you can earn and still be eligible for employment is an 84, what is the mean score for the exam? Round your answer to the nearest tenth. (12 points) 1 Instructions Instructions NAME: To complete the homework assignments in the templates provided: 1. The question is provided for each problem. You may need to refer to your textbook for additional information in a few cases. 2. You will enter the required information into the shaded cells. 3. The cells are coded: a) T requires a text answer. Essay questions require references; use the textbook. b) C requires a calculation, using Excel formulas or functions. You cannot perform the operation on a calculator and then type the answer in the cell. You will enter the calculation in the cell, and only the final answer will show in the cell. I will be able to review your calculation and correct, if necessary. c) F requires a number only. In some problems, a “Step 1” is added to help you solve the problem. d) Formula requires a written formula, not the numbers. For example, the rate of return = [(1 + nominal)/ (1+inflation)]-1, or D (debt) + E (equity) = V (value). 4. Name your assignment file as "lastnamefirstinitial-FINC600-Week#", and submit by midnight ET, Day 7. P7-2 Problem 7-2 The following table shows the nominal returns on U.S. Stocks and the rate of inflation: Year Nominal Return (%) Inflation (%) .5 3..4 3..8 2..6 4..2 0.1 a) What was the standard deviation of the market returns? b) Calculate the average real return. Answers: a) What was the standard deviation of the market returns? Find the standard deviation by completing the table with the appropriate formulas Year Nominal Return (%) Difference from Average Squared Difference TIP: Click on the cell for directions .5 C C .4 C C .8 C C .6 C C .2 C C Total C C Average C C Std. Deviation C Use SQRT function for this answer only b) Calculate the average real return. Find the average real return by completing the table with the appropriate formulas Year Nominal Return (%) Owner: Owner: You need to express as a percent in the calculation. For example, 12.5/100=.125 Inflation (%) Owner: Owner: Owner:You need to express as a percent in the calculation. For example, 3.3/100=.033 Real Return (%) Owner: Real return = [(1 +nominal)/(1+inflation)]-1 TIP: Click on the cell for directions .5 3.3 C .4 3.4 C .8 2.5 C .6 4.1 C .2 0.1 C Average C P7-11 Problem 7-11 Each of the following statements is dangerous or misleading. Explain why. a. A long-term United States government bond is always absolutely safe. b. All investors should prefer stocks to bonds because stocks offer higher long-run rates of return. c. The best practical forecast of future rates of return on the stock market is a 5- or 10-year average of historical returns. Answers: a. T b. T c. T Instructions: Please refer to your book for assistance with your homework. Post your work in the worksheet. Highlight your final answer. P8-6 Problem 8-6 Suppose that the Treasury bill rate were 6% rather than 4%. Assume that the expected return on the market stays at 10%. Use the betas in Table 8.2 (p. 193) - also provided below. a. Calculate the expected return from Dell. b. Find the highest expected return that is offered by one of these stocks. c. Find the lowest expected return that is offered by one of these stocks. d. Would Ford offer a higher or lower expected return if the interest rate were 6% rather than 4%? Assume that the expected market return stays at 10%. e. Would Exxon Mobil offer a higher or lower expected return if the interest rate were 8%? Answers: Formula Calculation A. Dell's expected return Rf + (Beta (Rm - Rf)) C B./C. Stock Beta (B) Revised T Bill Risk-Free Rate Market Return Expected return Amazon 2.16 F F C Ford 1.75 F F C Dell 1.41 F F C Starbucks 1.16 F F C Boeing 1.14 F F C Disney 0.96 F F C Newmont 0.63 F F C Exxon Mobil 0.55 F F C Johnson & Johnson 0.5 F F C Campbell Soup 0.3 F F C B. Highest T C. Lowest T D. FORD will offer a ________ expected return at 6%. Higher or lower? Interest rate 4% 6% Rate of return C C E. Exxon will offer a _______ expected return at 8%. Higher or lower? Interest rate 4% 8% Rate of return C C Instructions: Please refer to your book for assistance with your homework. Post your work in the worksheet. Highlight your final answer. Principles of Corporate Finance, Concise, 2nd Edition P8-18 Problem 8-18 Some true or false questions about the APT: a. The APT factors cannot reflect diversifiable risks. b. The market rate of return cannot be an APT factor. c. There is no theory that specifically identifies the APT factors. d. The APT model could be true but not very useful, for example, if the relevant factors change unpredictably. Respond to each question - true or false - and why. Answer: T/F a. WHY? b. WHY? c. WHY? d. WHY? Instructions: Please refer to your book for assistance with your homework. Post your work in the worksheet. Highlight your final answer.

Paper For Above instruction

The following analysis explores various statistical and financial concepts centered around normal distribution, probability, and investment risk assessment, based on the specified scenarios provided in the assignment prompt. The purpose of this paper is to demonstrate mathematical reasoning, interpretation, and application of these concepts in real-world contexts.

Question 1: Insurance Company Job Satisfaction Analysis

The first task analyzes the distribution of workers' job satisfaction scores within a large insurance firm. With a mean of 13.25 and a standard deviation of 1.6, assuming a normal distribution facilitates probability calculations essential for workforce management insights.

a) Probability between scores 14 and 18.5

To compute this probability, first calculate the z-scores for 14 and 18.5:

- \(z_{14} = \frac{14 - 13.25}{1.6} \approx 0.47\)

- \(z_{18.5} = \frac{18.5 - 13.25}{1.6} \approx 3.33\)

Using standard normal distribution tables or software, the cumulative probability for \(z_{14}\) is approximately 0.681, and for \(z_{18.5}\) approximately 0.9996. Therefore, the probability of a score falling between 14 and 18.5 is:

\[P(14

Interpretation: About 31.86% of workers are expected to have satisfaction scores within this range, indicating a significant portion experiences moderate to high satisfaction levels.

b) Number of very unhappy workers (score ≤ 9.0)

The z-score for 9.0:

- \(z = \frac{9 - 13.25}{1.6} \approx -2.66\)

The cumulative probability corresponding to \(z = -2.66\) is approximately 0.0039. Multiply by total workers:

- \(815 \times 0.0039 \approx 3.2\)

Approximately three workers are very unhappy, highlighting their rarity in the workforce distribution.

c) Minimum score for top 7%

Finding the score that corresponds to the 93rd percentile (since top 7% implies the 93rd percentile):

- \(z_{93} \approx 1.48\)

Using the z-score formula:

- \(X = \mu + z \times \sigma = 13.25 + 1.48 \times 1.6 \approx 13.25 + 2.37 = 15.62\)

Rounded to the nearest tenth, the minimum score is approximately 15.6. The percentile identified is the 93rd percentile, representing scores better than 93% of employees.

d) Score for bottom 2.5%

Find the z-score for the 2.5th percentile:

- \(z_{2.5} \approx -1.96\)

Calculate the score:

- \(X = 13.25 + (-1.96) \times 1.6 \approx 13.25 - 3.14 = 10.11\)

Rounded to the nearest tenth, a score of 10.1 or less indicates intensive counseling need, representing the lowest 2.5% of satisfaction scores.

Question 2: Remote Control Activation Distance Analysis

The second problem evaluates the percentage of users exceeding the remote's maximum range of 10 feet. With a mean of 6 feet and a standard deviation of 2.75 feet:

- Calculate the z-score for 10 feet:

\[

z = \frac{10 - 6}{2.75} \approx 1.45

\]

Using standard normal tables or software, the probability of a z-score exceeding 1.45 is approximately 0.0735, or 7.35%. Thus, approximately 7.35% of attempts occur outside the remote’s operational limit.

Question 3: Civil Service Exam Score Analysis

Given a standard deviation of 6.9, and eligibility for the top 5%, the cutoff is an 84 score. The z-score for the 95th percentile:

- \(z_{95} \approx 1.645\)

Applying the z-score formula:

- \(\text{Mean} = \frac{\text{score} - z \times \sigma}{1}\)

Rearranged:

- \(\text{Mean} = 84 - 1.645 \times 6.9 \approx 84 - 11.36 = 72.64\)

Rounded to the nearest tenth, the mean score for the exam is approximately 72.6, ensuring that scores above this are in the top 5%.

Discussion on Misleading Statements and Theoretical Concepts

Exploring the provided statements reveals the importance of context in financial risk assessment. The assertion that long-term government bonds are "absolutely safe" (a) neglects inflation risk and market fluctuations, making it false. The preference for stocks over bonds due to higher returns (b) ignores the higher volatility and risk, making this advice potentially misleading. For (c), averaging over a 5- or 10-year period is a practical heuristic, but it does not guarantee future performance due to market unpredictability. Regarding the Arbitrage Pricing Theory (APT) statements, the factors cannot reflect diversifiable risks directly (a) because these are inherently non-systematic. The market rate cannot be an APT factor (b), as APT uses macroeconomic factors, and the unavailability of all relevant factors (c) limits the model's precision. Finally, if relevant factors shift unpredictably (d), the usefulness of the APT diminishes because stability of factors is critical for reliable predictions.

Conclusion

This comprehensive analysis underscores the significance of statistical concepts in interpreting workplace satisfaction, consumer behavior, and investment risks. Accurate application of the normal distribution, z-scores, and percentiles provide vital insights for operational and strategic decision-making in various organizational contexts. Moreover, understanding the limitations of financial theories like the APT enhances prudent risk management, emphasizing the ongoing need for rigorous statistical literacy in finance and management practices.

References

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