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Measured Resistances 45,3 49,3 56,7 52,4 51,3 63,1 51,3 67,8 42,4 48,8 50,2 54,8 58,2 63,8 34,3 63,5 61,5 49,8 55,1 41,9 53,4 51,2 69,8 51,2 56,8 52,3 59,2 58,9 48,5 71,2 58,9 59,7 56,2 A resistor is a device that converts electrical energy into heat, causing the voltage to reduce as electrical current flows through the resistor. Resistors are extremely useful devices as they are found in nearly all electronic products. One way to make electrical resistors is to pack a plastic or ceramic tube with carbon powder and a suitable binder. Because it is very difficult to control the variables to get a precise resistance, manufacturers make a batch of resistors and measure the resistance of each one. Then, they are sorted and sold. At Resistors-R-Us (where the slogan is "You can't resist our resistors"), a large order was received for resistors that are 55 ± 5 Ω. A production run will be considered successful provided 80% of the resistors meet the specifications for the order. You are assigned the task of determining if the machine that makes resistors can successfully fill the order. To test the machine, you prepare a small batch of resistors. The data to the right shows the resistances, in ohms (Ω), measured for each resistor in the batch. Your tasks, to be completed in this Excel spreadsheet: 1. Create a copy of the data in a new column and sort the values from smallest to largest. Give this sorted list an appropriate name above the list's first value. 2. Prepare a frequency distribution table with classes that are 5 Ω wide (the first class is 30.0 to 34.9 Ω). Clearly label your table. 3. Prepare a histogram of the data. Give the histogram a title and label the axes appropriately. 4. Determine the following using excel functions (label each of these clearly): maximum, minimum, range, mode(s), median, mean, standard deviation, variance. 5. Assume the data can be described using a normal distribution and that a large production run will follow the same normal distribution as this sample data set. If 100,000 resistors are produced by this machine, how many will fall within the specification range of 55 ± 5 Ω? Use the norm.dist() function in Excel to assist in calculating this value, and be sure this value is clearly labelled. After calculating, write a sentence in your own words near your value stating whether this good enough to be considered successful based on the requirements for success described above. Notes: All calculations should be trackable in your submitted Excel file. You should not type in any values calculated outside of Excel or where the calculations cannot be found in the excel file. 57,2 56,3 61,3 39,8 63,1 60,4 59,7 67,3 58,9 59,3 55,5 67,5 45,8 63 68,2 53,2 65,1 53,2 62,4 43,8 46,7 38,9 56,8 The town council of Speedtrap is planning a budget for next year. The following table in blue shows the fines for speeding (which start with cars going 56 mph or faster). The mean speed of the automobiles on the highway is determined to be 52 mph and the standard deviation is 4 mph. The highway traffic is reported to be 200,000 automobiles each year. How much revenue is generated through speeding fines? Use the gray table on the right to populate the empty columns. Then calculate (using Excel) and clearly label the total revenue generated. Speed Range Max (mph) Speed Range Min (mph) Fine ($) $25,00 $50,00 $75,00 $100,00 $125,00 $150,00 $200,00 Area under Normal Curve for this speed range Quantity of Vehicles in the Speed Range out of 200 000 annual vehicles Revenue Generated 56 60 65 70 75 80 85 60 65 70 75 80 85 90 Speed (mph) 56–60 60–65 65–70 70–75 75–80 80–85 85–90 Fine $25 $50 $75 $100 $125 $150 $200 The decay of a radioactive element is described by the equation: A = A0e-kt where: A is the amount at time t, A0 is the amount at time zero, and k is the decay constant. The data in the table below were taken for the highly radioactive element balonium-245. Create properly labeled plots of the following in Excel: a) Balonium vs. Time using rectilinear axes. b) Naperian (natural) log of balonium vs. time using rectilinear axes. c) Balonium vs. Time using a semilog plot (using a base of 10 for the logarithmic scaled axis). d) Determine the constant, k. e) The half-life is defined as the time it takes for half of the balonium-245 to decay. Alternately, we could say it is the time at which half of the balonium-245 still remains, or A/A0 = 0.5. What is the half-life of balonium-245? Decay of balonium-245 Time (day) Balonium-245 (grams) 0,00 45,3 0,05 30,4 0,10 20,9 0,15 14,1 0,20 9,4 0,25 6,4 0,30 4,1 0,35 3,0 0,40 2,0 Constant, k = Balonium-245 half-life (day) = to do it on Excel. Do it on spradsheet of paper This For this one, don't have to on a paper.

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