solve these probability problems

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? Twenty adult males between the ages of 30 and 40 participated in a study to evaluate the effect of a specific health regimen involving diet and exercise on the blood cholesterol. Ten were randomly selected to be a control group, and ten others were assigned to take part in the regimen as the treatment group for a period of 6 months. The following data show the reduction in cholesterol experienced for the time period for the 20 subjects: Control group: 7 3 -4 14 2 522 -795 Treatment group: -6 5 9 4 4 12 37 5 3 3 (a) Do a dot plot of the data for both groups on the same graph. (b) Compute the mean, median, and 10% trimmed mean for both groups. (c) Explain why the difference in means suggests one conclusion about the effect of the regimen while the difference in medians or trimmed means suggests a different conclusion.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.An engineer desires to measure the thermal conductive ity of an aerogel material. It is expected that the aerogel will have an extremely small thermal conductivity. Heater leads -Coolant in Aerogel sample -Heater Aluminum plate (a) Explain why the apparatus of Problem 2.17 cannot be used to obtain an accurate measurement of the aerogel's thermal conductivity. (b) The engineer designs a new apparatus for which an electric heater of diameter D = 150mm is sand- wiched between two thin plates of aluminum. The steady-state temperatures of the 5-mm-thick alu- minum plates, 7, and 72, are measured with ther- mocouples. Aerogel sheets of thickness r = 5 mm are placed outside the aluminum plates, while a coolant with an inlet temperature of Ty, = 25"C maintains the exterior surfaces of the aerogel at a low temperature. The circular aerogel sheets are formed so that they encase the heater and alu- minum sheets, providing insulation to minimize radial heat losses. At steady state, 7, = , = 55"C. and the heater draws 125 mA at 10 V. Determine the value of the aerogel thermal conductivity ke. (c) Calculate the temperature difference across the thickness of the 5-mm-thick aluminum plates. Comment on whether it is important to know the axial locations at which the temperatures of the alu- minum plates are measured. (d) If liquid water is used as the coolant with a total flow rate of m = 1 kg/min (0.5 kg/min for each of the two streams), calculate the outlet temperature of the water, Tes.An investment firm offers its customers municipal bonds that mature after varying numbers of years. Given that the cumulative distribution function of 7, the number of years to maturity for a randomly selected bond, is t 3); (c) P(1.4 2).\f