In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two differentlots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient tofill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, theviscosity of batches consisting of two or more lots of material is more difficult to control, and 40% ofsuch batches require additional processing to achieve the required viscosity. Let A denote the event thata batch is formed from two different lots, and let B denote the event that a lot requires additionalprocessing. Determine the following probabilities:а. Р(А)e. P(ANB)f. P(ANB')g. P(B)b. P(А)С. Р[ВА)d. P(B|A')

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Answered: In the manufacturing of a chemical…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Persons having Raynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 9 subjects with the syndrome, the average heat output was x = 0.65, and for n = 9 nonsufferers, the average output was 2.03. Let μ1 and μ2 denote the true average heat outputs for the sufferers and nonsufferers, respectively. Assume that the two distributions of heat output are normal wit
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3. A tank contains 80 gals. of pure water. A brine solution with 2 lbs/gal of salt enters at 2 gals/min, and the well-stirred mixture leaves at the same rate. Find (a) the amount of salt in the tank at any time O a. 80 Ibs O b. 41.3 lbs c. 23 Ibs O d. 27.73 lbs
2.3 BP petrol is to be stocked in a bulk tank once at the beginning of each week and then sold to individual customers. Consider the joint density of Y,, the proportion of the capacity of the tank that is stocked at the beginning of the week and Y2, the proportion of the capacity sold during the week, given by fV1, Y2) = {3Y1, 0 < y2 < y1 < 1, elsewhere. In each week an average of 70% of the petrol is sold and an average of 30% of the petrol remains in the Caltex bulk tank at the end of each week. In any given week of the year, what is the probability that the amount of petrol sold during the week is more than the amount of petrol that was stocked in the beginning of the week?
a researcher collects a group of college students to determine the negative life events that they experienced in the past 5 years. For n=18 participants with 2 or fewer negative experiences, the average well being score is M=42 with SS=398, and for n=16 participants with 5 to 10 negative experiences the average well being score is M=48.6 with SS=370. A. Compute cohens d to measure the size of the effect.
2. Measurements were taken for entropy and enthalpy changes for many salts under a variety of water + methanol of NaCl (table salt) for several concentrations of methanol. Four independent conditions. The following table presents the results for enthalpy of transfer (in kJ/mol) from water to measurements were made at each concentration. Concentration (%) Enthalpy 1.62 1.60 1.62 1.66 5 10 20 30 2.69 2.66 2.72 2.73 3.56 3.45 3.65 3.52 3.35 3.18 3.40 3.06 a. Construct an ANOVA table in Excel. (8 points) b. Is it plausible that the enthalpy is the same at all concentrations? Explain. (4 points) No, brause the value is very low c. Use the Fisher LSD method to find a 95% confidence interval for the difference between the means for concentrations 5 and 30. Show your work. (12 points) d. Compute the quantity s = √MSE, the estimate of the standard deviation σ. (2 points)
A farmer has a 10-heactare maize farm. The maize is under “Fall Army Worm” attack. The farmer has to urgently control the attack using a chemical called AGENOX 221. Motorized sprayers with tank capacities of 15 litres each are to be used. The recommended concentration of the chemical is 2 ml/L and each full tank will cover ½ hectare. A 50-man team is engaged to control the attack. Using the above information and the assumptions given below: i. What volume of the chemical is required to cover the entire field to control the “Fall Army Worm” attack? ii. If each man covers an area of 25 meters square from one end of the field to the other, how many trips will each of them make to cover the entire field? Assume ach man moves in a straight line. Assumptions: 1. The 10 ha farm is considered to be a perfect square. 2. There is a 2.5 % loss of chemical due to the transfer to the sprayer tank.
A manufacturer is evaluating the variation in thickness for piezoelectric actuators from two component suppliers. The two populations are independent, and the thickness measurements are normally distributed. The thickness was measured for a sample of 30 products purchased from Supplier 1, and it was found that = 3.8048 . A sample of 30 products was also purchased from Supplier 2 and it was found that 5.2967. S1 S2 Is there evidence at the 0.1 level of significance that the thickness variance for Supplier 1 is smaller than for Supplier 2? (Round answers to 3 decimal places as needed) The correct alternative hypothesis is: O H1:0 + 0 OH1: H1 > µ2 : O H1:0} < o? O H1:0 2 0 O H1:0 O H1: µ1 2 l2 O H1: 41 < µ2 The test statistic is Fobs The probability of variance ratios at or beyond Fobs occurring by chance is = The decision is to Select an answer v that the variance in The correct summary would be: Select an answer thickness for Supplier 1 is smaller than Supplier 2.
Given the following grades on s test: 86, 92, 100, 93, 89, 95, 79, 98, 68, 62, 71, 75, 88, 86, 93, 81, 100, 86, 96, 52; What is the percentage of scores lying within one standard deviation from the mean? Two standard deviations from the mean? Are these results consistent with what
I. Evaluate the following antiderivatives.

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