solve these

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.A wealthy businessman wants to start a permanent fund for supporting research directed toward sus- tainability. The donor plans to give equal amounts of money for each of the next 5 years, plus one now (ie., six donations) so that $100,000 per year can be withdrawn each year forever, beginning in year 6. If the fund earns interest at a rate of 8% per year, how much money must be donated each time?At an interest rate of 10% per year, the capitalized cost of $10,000 in year 0, $5000 per year in years 1 through 5, and $1000 per year thereafter forever is closest to: (a) -$29,652 (b) -$35,163 (c) -$38 954 (d) -$43,221Let 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).Referring to Exercise 3.38, find (a) the marginal distribution of X; (b) the marginal distribution of Y. Reference: Exercise 3.38: If the joint probability distribution of X and Y is given by RX, y) = 30 Ity, for x = 0, 1, 2, 3; y = 0, 1, 2, find a) P(X $2, Y= 1); b) P(X >2, Y= 1); c) (c) P(X >Y):(d) P(X + Y = 4).Magnetron tubes are produced on an automated assembly line. A sampling plan is used periodically to assess quality of the lengths of the tubes. This measurement is subject to uncertainty. It is thought that the probability that a random tube meets length specification is 0.99. A sampling plan is used in which the lengths of 5 random tubes are measured. (a) Show that the probability function of Y , the number out of 5 that meet length specification, is given by the following discrete probability function: 5! f(y) = y!(5 - y)! (0.99)"(0.01)5-". (b) Suppose random selections are made off the line and 3 are outside specifications. Use fly) above either to support or to refute the conjecture that the probability is 0.99 that a single tube meets specifications