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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?Midwest Power and Light operates 14 coal-fired power plants in several states around the United States. The company recently settled a lawsuit by agreeing to pay $60 million in mitigation costs re- lated to acid rain. The settlement included $21 mil- lion to reduce emissions from barges and trucks in the Ohio River Valley, $24 million for projects to conserve energy and produce alternative energy, $3 million for Chesapeake Bay, $2 million for Shenandoah National Park, and $10 million to ac- quire ecologically sensitive lands in Appalachia. The question of how to distribute the money over time has been posed. Plan A involves spending $5 million now and the remaining $55 million equally over a 10-year period (that is, $5.5 million in each of years 1 through 10). Plan B requires ex- penditures of $5 million now, $25 million 2 years from now, and $30 million 7 years from now. De- termine which plan is more economical on the basis of a present worth analysis over a 10-year period at an interest rate of 10% per year.Two processes can be used for producing a poly- mer that reduces friction loss in engines. Process T will have a first cost of $750,000, an operating cost of $60,000 per year, and a salvage value of $80,000 after its 2-year life. Process W will have a first cost of $1,350,000, an operating cost of $25,000 per year, and a $120,000 salvage value after its 4-year life. Process W will also require updating at the end of year 2 at a cost of $90,000. Which process should be selected on the basis of a future worth analysis at an interest rate of 12% per year?For the density function of Exercise 3.18, find F(x), and use it to evaluate P(3 s X 2).Let X denote the number of times a certain numerical control machine will malfunction: 1, 2, or 3 times on any given day. Let Y denote the number of times a technician is called on an emergency call. Their joint probability distribution is given as f(x, y) 2 3 0.05 0.05 0.10 0.05 0.10 0.35 0.00 0.20 0.10 (a) Evaluate the marginal distribution of X. (b) Evaluate the marginal distribution of Y. (c) Find P(Y = 3 [ X = 2)