In the current tax year, suppose that 3% of the millions of individual tax returns have errors or are fraudulent. Although these errors are often well concealed, let’s suppose that a through IRS audit (done by you of course) will uncover them. If a random 100 tax returns are audited what is the probability that the IRS will uncover at most 4 fraudulent returns? Create an Excel spreadsheet that may give you an idea about this probability. Hint: Use the RAND() function for every tax return. The RAND() function generates a random number between 0 and 1. If the RAND() function gives you a number that is less than or equal to 0.03 then you can assume that the return contains error. Otherwise you can assume that the return does not contain any error. You can press F9 on your keyboard to regenerate a new instance. You may have to create enough instances to come up with a good approximation of the probability value. You can also find the exact probability using Binomial Distribution. What does it mean if an IRS auditor uncovers no more than 3 fraudulent/erroneous returns for every 100 tax returns?

Please in Excel.

You invest in $200 in the US stock market. If you hold it for one year, there is a 35% chance that your investment value will increase to $250, a 35% chance it will remain at $200, and a 30% chance it will decrease to $180

What is the mean annual return of the investment?

What is the annual return variance?

What is the annual return standard deviation?

Ethical Dilemma . Earlier this year, you were elected to the board of directors of Champion International, Inc. Champion has offered its employees post-retirement health care benefits for 35 years. The practice of extending health care benefits to retirees began modestly. Most employees retired after age 65, when most benefits were covered by Medicare. Costs also were lower because life expectancies were shorter and medical care was less expensive. Because costs were so low, little attention was paid to accounting for these benefits. The company simply recorded an expense when benefits were provided to retirees. The FASB changed all that. Now, the obligation for these benefits must be anticipated and reported in the annual report. Worse yet, the magnitude of the obligation has grown enormously, almost unnoticed. Health care costs have soared in recent years. Medical technology and other factors have extended life expectancies. Of course, the value to employees of this benefit has grown parallel to the growth of the burden to the company.

Without being required to anticipate future costs, many within Champion’s management were caught by surprise at the enormity of the company’s obligation. Equally disconcerting was the fact that such a huge liability now must be exposed to public view. Now you find that several board members are urging the dismantling of the postretirement plan altogether.

Required: Discuss whether the obligation to reduce the company's debt and employment expenses is greater than the obligation to employees to provide postretirement health benefits as a part of deferred compensation.

In a survey of 2508 2508 adults in a recent​ year, 1395 1395 say they have made a New​ Year's resolution. Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. The​ 90% confidence interval for the population proportion p is left parenthesis nothing comma nothing right parenthesis , . ​(Round to three decimal places as​ needed.) The​ 95% confidence interval for the population proportion p is left parenthesis nothing comma nothing right parenthesis , . ​(Round to three decimal places as​ needed.) With the given​ confidence, it can be said that the ▼ of adults who say they have made a New​ Year's resolution is ▼ between the endpoints less than the upper endpoint not between the endpoints greater than the lower endpoint of the given confidence interval. Compare the widths of the confidence intervals. Choose the correct answer below. A. The​ 90% confidence interval is wider. B. The​ 95% confidence interval is wider. C. The confidence intervals cannot be compared. D. The confidence intervals are the same width.

Suppose that a study shows that an electric bike is driven 23,500 km/year on average and has a standard deviation of 3900 km. Assume that the measurements’ distribution is approximately normal.

a) Calculate the 3rd quartile.

b) Solve for the probability that a randomly selected electric bike is driven at most 15,000 km per year, and then solve for the probability that a randomly selected electric bike is driven between 10,000 and 20,000 km per year.

c) If the average cost of leasing an electric bike is $300 per month with an SD of $110. You want to buy an electric bike so you randomly sample 20 people who are currently leasing. Solve for the probability that the sample mean, amongst the randomly selected 20 people, is less than $250.

d) Solve for the probability that the sample mean is greater than $300, amongst the randomly selected 20 people sampled in part c)

In May of the current year, your employer received a PIER report from the CRA that identified Canada Pension Plan (CPP) contribution deficiencies for employees in the organization who:

• turned 18 during the year
• turned 70 during the year
• had chosen to opt out of paying CPP by submitting a completed CPT30 form

To avoid a recurrence, the Payroll Manager, Sophie Beauchamp, has asked you to prepare a summary of the CPP reporting requirements on T4 information slips. The summary will be used to validate the current payroll setup to ensure that the T4s will be completed properly in future. Provide information on the CPP related boxes that must be completed, including how any amounts are calculated, for employees who:

• are under 18 for the entire year
• turn 18 during the year
• are over 70 for the entire year
• turn 70 during the year
• submit a completed CPT30 form during the year, electing to stop contributing to the Canada Pension Plan
• submit a completed CPT30 form during the year, revoking their previous election to stop contributing to the Canada Pension Plan

Births are approximately Uniformly distributed between the 52 weeks of the year. They can be said to follow a Uniform distribution from 1 to 53 (a spread of 52 weeks). Round answers to 4 decimal places when possible.

1. The mean of this distribution is
2. The standard deviation is
3. The probability that a person will be born at the exact moment that week 52 begins is P(x = 52) =
4. The probability that a person will be born between weeks 20 and 34 is P(20<x<34)P(20<x<34) =
5. The probability that a person will be born after week 14 is P(x > 14) =
6. P(x > 6 | x < 19) =
7. Find the 23rd percentile.
8. Find the minimum for the upper quartile.

6. Last year it was found that on average it took students 20 minutes to fill out the forms required for graduation. This year the department has changed the form and asked graduating student to report how much time it took them to complete the forms. Of the students 22 replied with their time, the average time that they reported was 18.5 minutes, and the sample standard deviation was 5.2. Can we conclude that the new forms take less time to complete than the older forms? Use a 0.1 significance level (i.e., p-value). (Assume that the reported times follow a Gaussian distribution)

Use the ERR method with   ? =%10 per year to solve a unique rate of return for the following cash flow diagram.