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Consider the drying time data for Exercise 1.1 on page 13. Compute the sample variance and sample standard deviation. Reference: Exercise 1.1 The following measurements were recorded for the drying tine. in hours. of a certain brand of latex pa'nt. 3.4 2.5 4.8 2.9 3.6 2.8 3.3 5.5 3.? 2.3 4.4 4.0 5.2 3.0 4.3 Assume that the measurements are a simple random sample. {a} What is the sample size for the above sample? {In} Calculate the sample mean for these data. {c} Calculate the sample median. {djl Plot the data by way of a dot plot. {e} Compute the 20% trirm'ned mean for the above data set. { Is the sample mean for these data more or less descriptive as a center of location than the trimmed mean? In a study conducted by the Department of Mechanical Engineering at Virginia Tech, the steel rods supplied by two different companies were compared. Ten sample springs were made out of the steel rods supplied by each company, and a measure of flexibility was recorded for each. The data are as follows: Company A: 9.3 8.8 6.8 8.7 8.5 6.7 8.0 6.5 9.2 7.0 Company B: 11.0 9.8 9.9 10.2 10.1 9.7 11.0 11.1 10.2 9.6 (a) Calculate the sample mean and median for the data for the two companies. (b) Plot the data for the two companies on the same line and give your impression regarding any apparent differences between the two companies. An overseas shipment of 5 foreign automobiles contains 2 that have slight paint blemishes. If an agency receives 3 of these automobiles at random, list the elements of the sample space S, using the letters Band / for blemished and nonblemished, respectively; then to each sample point assign a value x of the random variable X representing the number of automobiles with paint blemishes purchased by the agency.The Murphy County Fire Department is consider- ing two options for upgrading its aging physical fa- cilities. Plan A involves remodeling the fire stations on Alameda Avenue and Trowbridge Boulevard that are 57 and 61 years old, respectively. (The industry standard is about 50 years of use for a station.) The cost for remodeling the Alameda station is esti- mated at $952,000 while the cost of redoing the Trowbridge station is $1.3 million. Plan B calls for buying 5 acres of land somewhere between the two stations, building a new fire station, and selling the land and structures at the previous sites. The cost of land in that area is estimated to be $366,000 per acre. The size of the new fire station would be 9000 square feet with a construction cost of $151.18 per square foot. Contractor fees for overhead, profit, etc. are expected to be $140,000, and architect fees will be $81,500. (Assume all of the costs for plan B occur at time 0.) If plan A is adopted, the extra cost for personnel and equipment will be $126,000 per year. Under plan B, the sale of the old sites is antici- pated to net a positive $500,000 five years in the future. Use an interest rate of 6% per year and a 50- year useful life for the remodeled and new stations to determine which plan is better on the basis of a present worth analysis.A pipeline engineer working in Kuwait for the oil giant BP wants to perform a present worth analysis on alternative pipeline routings-the first predominately by land and the second primarily undersea. The un- dersea route is more expensive initially due to extra corrosion protection and installation costs, but cheaper security and maintenance reduces annual costs. Per- form the analysis for the engineer at 15% per year.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?The probability distribution of X, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width, is given by 1 2 3 I(x) 0.41 0.37 0.16 0.05 0.01 Construct the cumulative distribution function of X. Let X denote the diameter of an armored electric cable and Y denote the diameter of the ceramic mold that makes the cable. Both X and Y are scaled so that they range between 0 and 1. Suppose that X and Y have the joint density f (z, y) = - 01/2).Classify the following random variables as discrete or continuous: X: the number of automobile accidents per year in Virginia. Y: the length of time to play 18 holes of golf. M: the amount of milk produced yearly by a particular cow. N: the number of eggs laid each month by a hen. P. the number of building permits issued each month in a certain city. Q: the weight of grain produced per acre