A manufacturing company employs two devices to inspect output for quality control purposes. The first device is able to accurately detect 99.3% of the defective items it receives, whereas the second is able to do so in 99.7% of the cases. Assume that four defective items are produced and sent out for inspection. Let X and Y denote the number of items that will be identified as defective by inspecting devices 1 and 2, respectively. Assume that the devices are independent. Determine fxy(X=4) Determine E(X) Determine VY|X=2).
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- Your company manufactures plastic wrap for food storage. The tear resistance of the wrap, denoted by X, must be controlled so that the wrap can be torn off the roll without too much effort but it does not tear too easily when in use. In a series of tests (see data table below), 15 rolls of wrap are made under carefully controlled conditions and the tear resistance of each roll is measured. The results are used as the basis of a quality assurance specification. If X for a subsequently produced roll falls more than two standard deviations away from the test period average, the process is declared out of specification and production is suspended for routine maintenance. Roll 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 X 134 131 129 133 135 131 134 130 131 136 129 130 133 130 133 Write an Excel spreadsheet to calculate the sample mean and sample standard deviations. The {#1} {#2} a)What…A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 10 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 10 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 2.6, 5.9, 5.3, 5.8, 8.7, 6.2, 7.6, 6.4, 8.0, 4.0 Treated with placebo 3.0, 5.1, 4.7, 4.2, 4.7, 5.6, 5.9, 4.7, 7.1, 4.9 It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, l, of the patients treated…A) Classify the following data as either qualitative data or quantitative data. In addition, classify the quantitative data as discrete or continuous. The number of times that a movement authority is sent to a train from a relay station is recorded for several trains Over a three-week period. The movement authority, which is an electronic transmission, is sent repeatedly until a return signal is received from the train. 1. 2. A physician records the follow-up condition of patients with optic neuritis as improved, unchanged, or worse. The individuals in a sociological study are classified into one of five income classes as follows: low, low to middle Middle, middle to upper, or upper. 3.
- Suppose that a study was conducted to determine if there is a significant difference in the average temperature of individuals before and after COVID-19 boosters were given. The temperatures of a sample of individuals were obtained before the boosters were given. The following day, their temperatures were again measured. The table below shows the data in degrees Celsius. (10 points) Temperature before Temperature after one day. Determine If there is a significant difference in the average temperature of Individuals who were given boosters at 5% level of significance. Assume that the differences in the temperatures follow the normal distribution.What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 16.1 22.7 25.3 1.98 32.2 38.3 51.3 20.5 y 2.78 1.88 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex, Ey", Exy, and r. (Round r to three decimal places.) Ex= Ey= Ey? - Exy = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) critical t= Conclusion O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. Reject the null hypothesis. There is sufficient evidence that p < 0. Reject the null hypothesis.…What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data.x 12.1 26.3 32.2 38.3 51.3 20.5 22.7y 2.48 2.18 1.48 1.03 0.75 2.38 2.20 a) Find the predicted optimal time in hours for a dive depth of x = 22 meters. (Round your answer to two decimal places.)______ hr b) Find an 80% confidence interval for y when x = 22 meters. (Round your answers to two decimal places.)lower limit= ____ hrupper limit =____hr c) Find a 90% confidence interval for ? and interpret its meaning. (Round your answers to three decimal places.)lower limit =upper limit=
- Z.5 points A dependent t-test study and an independent t-test study both produced a t statistic with df = 10. How many individuals participated in each study? 12 for dependent and 12 for independent 12 for the dependent and 11 for independent 11 for dependent and 11 for independent 11 for dependent and 12 for independentSuppose that we have a data set of college students. This data set includes whether each student graduated with honors and whether the same student went to graduate schools to pursue a PhD degree. Assume that P({Graduate w/ honors} ∩ {Pursusing PhD}) = P({Graduate w/ honors}) x P({Pursuing PhD}) Pursu PhD Not Pursu PhD Total Grad w/ honors x1 x2 0.25 Grad w/o honors x3 x4 0.75 Total 0.20 0.80 What is (x1 + x4) - (x2 + x3) 0.20 0.25 0.30 0.35 What is P({Graduate w/ honors} | {Pursuing PhD})? 0.20 0.25 0.50 0.752) d and e.
- What is the optimal time for a scuba diver to be on the bottom of the ocean? That depends on the depth of the dive. The U.S. Navy has done a lot of research on this topic. The Navy defines the "optimal time" to be the time at each depth for the best balance between length of work period and decompression time after surfacing. Let x = depth of dive in meters, and let y = optimal time in hours. A random sample of divers gave the following data. 15.1 26.3 31.2 38.3 51.3 20.5 22.7 y 2.68 2.38 1.48 1.03 0.75 2.38 2.20 (a) Find Ex, Ey, Ex², Ey², Exy, and r. (Round r to three decimal places.) Σχ = Ey = Ex? = Ey? = Σχy r = (b) Use a 1% level of significance to test the claim that p < 0. (Round your answers to two decimal places.) t = critical t = Conclusion O Fail to reject the null hypothesis. There is insufficient evidence that p < 0. O Fail to reject the null hypothesis. There is sufficient evidence that p < 0. O Reject the null hypothesis. There is insufficient evidence that p < 0. O…12) The data are the maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. maximum daily temperatures at Cox-Dayton International Airport for June and July 2018. Date Max (°F) Jun 1 80 Jun 2 82 Jun 3 81 Jun 4 75 Jun 5 76 Jun 6 71 Jun 7 82 Jun 8 85 Jun 9 86 Jun 10 77 Jun 11 75 Jun 12 78 Jun 13 85 Jun 14 82 Jun 15 86 Jun 16 90 Jun 17 92 Jun 18 92 Jun 19 89 Jun 20 85 Jun 21 72 Jun 22 81 Jun 23 79 Jun 24 85 Jun 25 79 Jun 26 79 Jun 27 81 Jun 28 85 Jun 29 89 Jun 30 92 Jul 1 93 Jul 2…A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin Treated with placebo 3.0, 5.6, 1.5, 6.8, 3.8, 7.5, 5.8, 4.6, 2.4, 5.0, 7.5, 5.0, 2.6, 1.7, 6.7 4.9, 6.1, 4.9, 4.2, 3.4, 5.5, 5.6, 3.4, 7.9, 6.8, 4.8, 4.2, 5.7, 2.2, 4.0 Send data to Excel Send data to calculator It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally…