Distinguish between a progressive tax system and a regressive tax system. Consider two categories of people—the rich and the poor. Who—the rich or the poor—pay more tax under a progressive tax system? Who pay more tax under a regressive tax system? Who pay a higher percentage of their taxable income under a progressive tax system? And who pay a higher percentage of their taxable income under a regressive tax system?

The heights of newborn babies have a symmetric distribution with a mean of 20 inches and a SD of 2 inches. Find the percentage of newborn babies whose height is between 18 inches and 22 inches

Answer the following questions:

• Do you apply Chebyshev’s Theorem or OR Empirical Rule?
• What is K? Remember that “k” is the number of standard deviation from the mean?
• The percentage of newborn babies whose height is between 18 inches and 22 inches is:

Company A is presenting following figures concerning their business:

Planned production volume: 2 000 units

Variable costs/unit:

material                      900 €

labor               1 200 €

other necessities         400 €

Fixed costs:               1 500 000 €

Sales price per unit:               4 000 €

Calculate:

result of the business according to budget

break even point

margin of safety

margin of safety (percentage)

contribution margin

contribution margin (percentage)

The results of the test given to students are assume to be normally distributed with a mean of 57 and a standard deviation of 10. The passing score for the exam is 30.  Answer in figure only.

a) If a student is randomly selected, what is the probability that he or she passed the exam? Answer in 4 decimal places. Answer in percentage in in 2 decimal places.

b) A score of 75 or greater is needed to obtain an A on the exam. What percentage of the students received an A? Answer in 2 decimal places.

In a certain state the recent average critical reading standardized test score was 481. Assume that the standard deviation is 50 and that standardized test scores are Normally distributed. Include an appropriately labeled and shaded Normal curve for each part. Complete

Include a Normal curve for each part.

a. What percentage of standardized test takers scored between 400 and 500? _______

b. What percentage of standardized test takers scored between 500 and 600? _______

Consider a 8% coupon bond making annual coupon payments with 4 years until maturity and a yield to maturity of 10%.

1. What is the modified duration of this bond?

2. If the market yield increases by 75 basis points, what is the actual percentage change in the bond’s price? [Actual, not approximation]

3. Given that this bond’s convexity is 14.13, what price would you predict using the duration-with-convexity approximation for this bond at this new yield?

4. What is the percentage error?

For bone density scores that are normally distributed with a mean of 0 and a standard deviation of​ 1, find the percentage of scores that are a. significantly high​ (or at least 2 standard deviations above the​ mean). b. significantly low​ (or at least 2 standard deviations below the​ mean). c. not significant​ (or less than 2 standard deviations away from the​ mean).

a. The percentage of bone density scores that are significantly high is nothing​%. ​(Round to two decimal places as​ needed.)

A survey found that​ women's heights are normally distributed with mean 62.9 in. and standard deviation 3.8 in. The survey also found that​ men's heights are normally distributed with mean 67.8 in. and standard deviation 3.5 in. Consider an executive jet that seats six with a doorway height of 56.4 in. Complete parts​ (a) through​ (c) below. a. What percentage of adult men can fit through the door without​ bending? The percentage of men who can fit without bending is?

Bond J has a coupon of 4.2 percent. Bond K has a coupon of 8.2 percent. Both bonds have 10 years to maturity and have a YTM of 6 percent.

a. If interest rates suddenly rise by 1 percent, what is the percentage price change of these bonds?

Bond J:

Bond K:

b. If interest rates suddenly fall by 1 percent, what is the percentage price change of these bonds?

Bond J:

Bond K: