solve the following question

The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint. 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.6 3.7 2.8 4.4 4.0 5.2 3.0 4.8 Assume that the measurements are a simple random sample. (a) What is the sample size for the above sample? (b) Calculate the sample mean for these data. (c) Calculate the sample median. (d) Plot the data by way of a dot plot. (e) Compute the 20% trimmed mean for the above data set. (f) Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean?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.The initial cost of a bridge that is expected to be in place forever is $70 million. Maintenance can be done at 1-, 2-, 3-, or 4-year intervals, but the longer the interval between servicing, the higher the cost. The costs of servicing are estimated at $83,000, $91,000, $125,000, and $183,000 for intervals of 1 through 4 years, respectively. What interval should be scheduled for maintenance to minimize the overall equivalent annual cost? The interest rate is 8% per year. A construction company bought a 180,000 metric ton earth sifter at a cost of $65,000. The company expects to keep the equipment a maximum of 7 years. The operating cost is expected to follow the series described by 40,000 + 10,000k, where & is the number of years since it was purchased (* = 1, 2, . . ., 7). The salvage value is estimated to be $30,000 for years 1 and 2 and $20,000 for years 3 through 7. At an interest rate of 10% per year, deter- mine the economic service life and the associated equivalent annual cost of the sifter. An engineer determined the ESL of a new $80,000 piece of equipment and recorded the calculations shown below. [Note that the num- bers are annual worth values associated with various years of retention; that is, if the equip- ment is kept for, say, 3 years, the AW (years 1 through 3) of the first cost is $32,169, the AW of the operating cost is $51,000, and the AW of the salvage value is $6042.] The engineer forgot to enter the AW of the salvage value for 2 years of retention. From the information available, deter- mine the following: (a) The interest rate used in the ESL calculations. (b) The salvage value after 2 years, if the total AW of the equipment in year 2 was $78,762. Use the interest rate determined in part (a).A recent environmental engineering graduate is try- ing to decide whether he should keep his presently owned car or purchase a more environmentally friendly hybrid. A new car will cost $26,000 and have annual operation and maintenance costs of $1200 per year with an $8000 salvage value in 5 years (which is its estimated economic service life). The presently owned car has a resale value now of $5000; one year from now it will be $3000, two years from now $2500, and 3 years from now $2200. Its operating cost is expected to be $1900 this year, with costs increasing by $200 per year. The presently owned car will definitely not be kept longer than 3 more years. Assuming used cars like the one presently owned will always be available, should the presently owned car be sold now, 1 year from now, 2 years from now, or 3 years from now? Use annual worth calculations at i = 10% per year and show your work. A pulp and paper company is evaluating whether it should retain the current bleaching process that uses chlorine dioxide or replace it with a proprie- tary "oxypure" process. The relevant information for each process is shown. Use an interest rate of 15% per year to perform the replacement study. Current Process Oxypure Process Original cost 6 -450,000 years ago, $ Investment cost -700,000 now, $ Current market 25,000 value, $ Annual operating - 180,00 0 -70,000 cost, $/year Salvage value, $ 50,000 Remaining life, 10 yearsFind the probability distribution for the number of jazz CDs when 4 CDs are selected at random from a collection consisting of 5 jazz CDs, 2 classical CDs, and 3 rock CDs. Express your results by means of a formula. A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter would be 570 mm. The data are as follows: 572, 572, 573, 568, 569, 575, 565, 570. (a) Find the sample mean and median. (b) Find the sample variance, standard deviation, and range. (c) Using the calculated statistics in parts (a) and (b), can you comment on the quality of the tires?Three cards are drawn in succession from a deck without replacement. Find the probability distribution for the number of spades. Find a formula for the probability distribution of the random variable X representing the outcome when a single die is rolled once. Find the probability distribution of the random variable Win Exercise 3.3, assuming that the coin is biased so that a head is twice as likely to occur as a tail. Reference: Exercise 3.3: 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.\f