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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? Let Wbe a random variable giving the number of heads minus the number of tails in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W.An electric switch manufacturing company has to choose one of three different assembly methods. Method A will have a first cost of $40,000, an an- nual operating cost of $9000, and a service life of 2 years. Method B will cost $80,000 to buy and will have an annual operating cost of Sholl over its 4-year service life. Method C will cost $130,000 initially with an annual operating cost of $4000 over its 8-year life. Methods A and B will have no salvage value, but method C will have some equip- ment worth an estimated $12,000. Which method should be selected? Use present worth analysis at an interest rate of 10% per year.Two manufacturers supply MRI systems for medi- cal imaging St. Jude's Hospital wishes to replace its current MRI equipment that was purchased & years ago with the newer technology and clarity of a state- of-the-art system. System K will have a first cost of $1,600,000, an operating cost of $70,000 per year, and a salvage value of $400,000 after its 4-year life. System L will have a first cost of $2,100,000, an operating cost of $50,000 the first year with an ex- pected increase of $3000 per year thereafter, and no salvage value after its 8-year life. Which system should be selected on the basis of a future worth analysis at an interest rate of 12% per year?Consider a small but known volume of metal that has a large thermal conductivity. (a) Since the thermal conductivity is large, spatial temperature gradients that develop within the metal in response to mild heating are small. Neglecting spatial temperature gradients, derive a differential equation that could be solved for the temperature of the metal versus time 7() if the metal is sub- jected to a fixed surface heat rate q supplied by an electric heater. (b) A student proposes to identify the unknown metal by comparing measured and predicted thermal responses. Once a match is made, relevant thermo- physical properties might be determined, and, in turn, the metal may be identified by comparison to published property data. Will this approach work? Consider aluminum, gold, and silver as the candi- date metals.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).The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Suppose that the tank is not resupplied during the day so that x sy, and assume that the joint density function of these variables is 12, 0 0, y>0, elsewhere, Find -(sty). r>0, y>0, f(x,y) = 10, elsewhere