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Compute the sample variance and standard deviation for the water absorbency data of Exercise 1.2 on page 13. Reference: Exercise 1.2 According to the journal Chemical Engineering, an important property of a fiber is its water absorbency. A random sample of 20 pieces of cotton fiber was taken and the absorbency on each piece was measured. The following are the absorbency values: 18.71 21.41 20.72 21.81 19.29 22.43 20.17 23.71 19.44 20.50 18.92 20.33 23.00 22.85 19.25 21.77 22.11 19.77 18.04 21.12 (a) Calculate the sample mean and median for the above sample values. (b) Compute the 10% trimmed mean. (c) Do a dot plot of the absorbency data. (d) Using only the values of the mean, median, and trimmed mean, do you have evidence of outliers in the data?A public corporation in which you own common stock reported a WACC of 11.1% for the year in its report to stockholders. The common stock that you own has averaged a total return of 7% per year over the last 3 years. The annual report also men- tions that projects within the corporation are 75% funded by its own capital. Estimate the company's cost of debt capital. BASF will invest $14 million this year to upgrade its ethylene glycol processes. This chemical is used to produce polyester resins to manufacture products varying from construction materials to aircraft, and from luggage to home appliances. Eq- uity capital costs 14.5% per year and will supply 65% of the capital funds. Debt capital costs 10% per year before taxes. The effective tax rate for BASF is 36% (a) Determine the amount of annual revenue after taxes that is consumed in covering the interest on the project's initial cost. (b) If the corporation does not want to use 65% of its own funds, the financing plan may in- clude 75% debt capital. Determine the amount of annual revenue needed to cover the interest with this plan, and explain the ef- fect it may have on the corporation's ability to borrow in the future. A couple planning for their child's college educa- tion can fund part of or all the expected $100,000 tuition cost from their own funds (through an edu- cation IRA) or borrow all or part of it. The average return for their own funds is 7% per year, but the loan is expected to have a higher interest rate as the loan amount increases. Use a spreadsheet to generate a plot of the WACC curve with the esti- mated loan interest rates below and determine the best D-E mix for the couple.A proposal to reduce traffic congestion on 1-5 has a B/C ratio of 1.4. The annual worth of benefits minus disbenefits is $560,000. What is the first cost of the project if the interest rate is 6% per year and the project is expected to have a 20-year life? Oil spills in the Gulf of Mexico have been known to cause extensive damage to both public and pri- vate oyster grounds along the Louisiana and Mis- sissippi shores. One way to protect shellfish along the shoreline is to release large volumes of fresh- water from the Mississippi River to flush oil out to sea. This procedure inevitably results in death to some of the saltwater shellfish while preventing more widespread destruction to public reefs. Oil containment booms and other temporary struc tures can also be used to intercept floating oil be- fore it damages sensitive fishing grounds. If the Fish and Wildlife Service spent $110 million in year 0 and $50 million in years 1 and 2 to mini- mize environmental damage from one particular oil spill, what is the benefit-to-cost ratio provided the efforts resulted in saving 3000 jobs valued at a total of $175 million per year? Assume disbenefits associated with oyster deaths amounted to $30 mil- lion in year 0. Use a 5-year study period and an interest rate of 8% per year. On-site granular ferric hydroxide (GFH) systems can be used to remove arsenic from water when daily flow rates are relatively low. If the operating cost is $600,000 per year and the public health benefits are assumed to be $800,000 per year, what initial investment in the GFH system is necessary to guarantee a modified B/C ratio of at least 1.0? Assume that the equipment life is 10 years and the interest rate is 6% per year.For the density function of Exercise 3.17, find F(x). Use it to evaluate P(2