Mechanical Engineering Department ME 406 Manufacturing and Design First Semester 2017 (Term-171) HOMEWORK # 2 (Engineering Statistics) Assigned by: Dr. Anwar K. Sheikh/Dr Numan Abu Dheir Assigned on Sunday 15th October 2017, Due on Sunday (in class), 22nd October 2017 Must provide a standard cover sheet on your solution. Also start each question on a separate page .Provide problem statement of the top of each of your solution page. Problem # 1 1.1 Consider a normally distributed random variable X with mean = 20, and standard deviation = 30. Compute the following probabilities? 1. P[ X >80] 2. P[ X 80 ] 3. P[ X 80] 4. P[50 X 80] 1.2 If X is normally distributed with mean and standard deviation four, and given that the probability that X is less than 32 is 0.0228, find the value of ? Problem # 2 Problem # 2.1 The output voltage of a power supply is normally distributed with mean 12 V and standard deviation 0.10 V. If the upper and lower specifications for voltage are 11.85 V and 12.15 V, respectively, what is the probability that a power supply selected at random will conform to the specifications on voltage? Problem # 3 Problem # 3.1 The life of an automotive battery is normally distributed with mean 900 days and standard deviation 50 days. What fraction of these batteries would be expected to survive beyond 1000 days? Problem # 3.2 A light bulb has a normally distributed light output with mean 3000 end foot-candles and standard deviation of 50 end foot-candles. Find a lower specification limit such that only 0.5% of the bulbs will not exceed this limit. Problem # 4 The shear strengths of 100 spot welds in a titanium alloy follow. 5408 5431 5475 5442 5376 5388 5459 5422 5416 5435 5420 5429 5401 5446 5487 5416 5382 5357 5388 5457 5407 5469 5416 5377 5454 5375 5409 5459 5445 5429 5463 5408 5481 5453 5422 5354 5421 5406 5444 5466 5399 5391 5477 5447 5329 5473 5423 5441 5412 5384 5445 5436 5454 5453 5428 5418 5465 5427 5421 5396 5381 5425 5388 5388 5378 5481 5387 5440 5482 5406 5401 5411 5399 5431 5440 5413 5406 5342 5452 5420 5458 5485 5431 5416 5431 5390 5399 5435 5387 5462 5383 5401 5407 5385 5440 5422 5448 5366 5430 5418 Construct a cumulative frequency plot and histogram for above the weld strength data (a) Use 8 bins.(cells) (b) Use 16 bins and compare with part (a). Problem # 5 Problem # 6 Problem # 7 7.1 2-5. An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen.The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72,50.77, 39.30, and 49.71. Calculate the sample average and sample standard deviation. Construct a dot diagram of the data. 7.2 2-6. Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate fatigue crack in n _ 9 cyclically loaded wing boxes reported the following crack lengths (in mm) 2.13, 2.96, 3.02, 1.82, 1.15, 1.37, 2.04, 2.47, and 2.60. Calculate the sample average and sample standard deviation.Construct a dot diagram of the data. Problem # 8 Concentration of pollutants produced by chemical plants historically is known to exhibit a lognormal distribution. If he concentration of a certain pollutant, X in parts per million, has a lognormal distribution with parameters = 3 and w = 1.What is the probability that the concentration exceeds 10 parts per million? Problem # 9 A manufacturer of sports equipment has developed a new synthetic fishing line that he claims has a mean breaking strength of 8 kilograms with a standard deviation of 0.5 kilogram. Test the hypothesis that = 8 kilograms against the alternative that 8 kilograms if a random samples of 50 lines is tested and found to have a mean breaking strength of 7.8 kilograms, Use a 0.01 level of significance. Problem # 10 The Edison Electric Institute has published figures of the annual number of kilowatt-hours expended by various home appliances. It is claimed that a vacuum cleaner expends an average of 46 kilowatt-hours per hear. If a random sample of 12 homes included in a planned study indicates that vacuum cleaner expend an average of 42 kilowatt-hour per year with a standard deviation of 11.9 kilowatt-hours, does this suggest at the 0.05 level significance that vacuum cleaner expend, on the average, less than 46 kilowatt-hours annually? Assume the population of kilowatt-hours to be normal. Problem # 11 An experiment was performed to compare the abrasive wear of two different laminated materials. Twelve pieces of material 1 were tested by exposing each piece to a machine measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth of wear was observed. The samples of material 1 gave an average (coded) wear if 85 units with a sample standard deviation of 5. Can we conclude at the 0.05 level of significance that the abrasive wear of material 1 exceeds that of material 2 by more than 2 units? Assume the populations to be approximately normal with equal variances. Problem # 12 The inside diameters of bearings produced by a certain manufacturing process are known to have a standard deviation of = 0.0001 cm. A random sample of 15 bearings has an average inside diameter of 8.2535 cm. Construct a 95% two-sided confidence interval on the mean bearing diameter. Problem # 13 The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 2 psi. A random sample of eight fiber specimens selected and the average tensile strength is found to 127 psi. Construct a 95% lower confidence limit of the mean tensile strength. Problem # 14 A filling machine is set to fill packages to a certain weight (w) . Sixteen packages were chosen at random; their average weight ( w) was found to be 95 oz, and the standard deviation 4.00 oz. Estimate the population mean (s ) with 90% confidence. Problem # 15 Formulate the appropriate null and alternative hypotheses to test the following claims. (a) A plastics production engineer claims that 99.95% of the plastic tube manufactured by her company meets the engineering specifications requiring the length to exceed 6.5 inches. (b) A chemical and process engineering team claims that the mean temperature of a resin bath is greater than 45C. (c) The proportion of start-up software companies that successfully market their product within 3 years of company formation is less than 0.05. (d) A chocolate bar manufacturer claims that, at the time of purchase by a consumer, the mean life of its product is less than 90 days. (e) The designer of a computer laboratory at a major university claims that the standard deviation of time of a student on the network is less than 10 minutes. (f ) A manufacturer of traffic signals advertises that its signals will have a mean operating life in excess of 2160 hours