3. Ophthalmic lens is used in optical device to enhance vision addressing the visual needs of theindividual wearer. Two different polishing solutions can be used for polishing the ophthalmiclenses. 350 lenses were polished using the first polishing-solution, and of this number, 294had no polishing-induced defects. Another 400 lenses were polished using the secondpolishing solution, and 74 lenses had polishing-induced defects.i.Construct a 95% confidence interval on the difference of the proportion polishing-induced defects between the first and second polishing solutions.UTMii.Based on the result in part (i), is there any indication that both types of polishingsolutions have different effect on the ophthalmic lens? Justify your answer.OUTHUTM

Confidence interval are used to examine the range where the population parameter can occur. It has…

Answered: 3. Ophthalmic lens is used in optical…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
The Pretty Cat Company wishes to introduce a new brand of cat dry foods that meets certain nutritional requirements. The biscuit-1 contains 2 units of nutrient A and 4 units of nutrient B, while biscuit-2 contains 2 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 80 units of nutrient A and 120 units of nutrient B in a package of the new dry food (biscuit mix). In addition, the company has decided that there can be no more than 30 biscuit-1 in a package. If it costs 2 cents to make a biscuit-1 and 4 cents to make a biscuit-2, what is the optimal product mix for a package of the new dry food in order to minimize the firm's cost? (a) Formulate this as a linear programming problem. (b) Find the optimal solution for this problem graphically. What is the total cost of a package of the new dry food using the optimal mix?
Two different types of polishing solutions are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery. Three hundred lenses were tumble polished using the first polishing solution, and ofthis number, 253 had no polishing-induced defects. Another 300 lenses were tumble-polishedusing the second polishing solution, and 196 lenses were satisfactory upon completion.(a) Is there any reason to believe that the two polishing solutions differ? Use α = 0.01
choose one of the following procedures for each of the research scenarios described. In a rural school 202 students from a total school population of 723 suffer from malnutrition while in an urban school, 167 students from a total of 1 001 suffer from malnutrition. A master’s degree student wants to determine whether suffering from malnutrition is dependent on the region (urban versus rural) in which the school is situated.
Kentville, a community of 10,000 people, resides next to a krypton mine, and there is a concern that the emission from the krypton smelter have resulted in adverse effects. Specifically, Kryptonosis seems to have killed 12 of Kentville’s inhabitants last year. A neighboring community, Lanesburg, has 25,000 inhabitants and is far enough from the smelter to not be affected by the emission. In Lanesburg, only three people last year died of Kryptonosis. Given that the number of deaths in Kentville and their causes last year were: Heart attack=7 Accidents=4 Kryptonosis=12 Other=6 What is the risk of dying of Kryptonosis in Kentville relative to non-contaminated locality?What is the risk of dying of Kryptonosis in Kentville relative to deaths due to other causes? How many times the chance of dying of Kryptonosis compared to dying of accidents ? How many times the chance of dying of Kryptonosis compared to Other causes?
Cecille Paper Company uses softwood and hardwood pulp as basic materials for producing converter-grade paper. Hardwood is 80% pulp fiber and 20% pulp binder, while softwood is 50% pulp fiber and 50% pulp binder. The cost per pound for hardwood and softwood is $.50 and $.40, respectively. The company s quality control expert specifies that in order for the product to meet quality standards, each batch must contain at least 12,000 pounds of pulp fiber and at least 6,000 pounds of pulp binder. Because of equipment limitations, the size of a batch cannot exceed 24,000 pounds. The Production Department recently received a new standard from the Cost Department, allowing $8,200 per batch. The production manager feels that this amount is too low, because such costs have never been less than $8,400. Required: Using the graphic method, determine the hardwood and softwood mix necessary to minimize the cost per batch.
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In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 73% of the valves meet the specification, 21% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 46% meet the specification, and 54% are scrapped. Given that a valve meets the specification, what is the probability that it was ground only once?
A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada. Production records show that the U.S. plants each produced 10,000 snowboards last month, while the Canadian plant produced 8000 boards. Of all the boards manufactured in Canada last month, 4% had a defect that caused the boards to delaminate prematurely. Records kept at the U.S. plants show that 3% of the boards manufactured in the eastern United States and 6% of the boards manufactured in the western United States had this defect as well. a) What proportion of the boards manufactured last month were defective? b) What is the probability that a snowboard is defective and was manufactured in Canada? c) Given that a snowboard is defective, what is the probability that it was manufactured in the United States?
Use complementary slackness and the solution to its dual problem to find solution(s) to the primal LPP.
An existing mall (Circuit Mall) is located near the residential area and has the following characteristics: Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) Circuit Mall 2.1 220 Three malls are to be built to rival the existing mall and there are currently three proposals. A total of 5000 shopping trips are generated from the residential area. Use n=1.5 Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) SM City 1 3.25 150 SM City 2 5.68 300 SM City 3 6.75 600 How many trips would Circuit Mall make compared to the new competitors?
In a large metropolitan area, 20% of the commuters currently use the public transportation system, whereas the remaining 80% commute via automobile. The city has recently revitalized and expanded its public transportation system. It is expected that 6 months from now 30% of those who are now commuting to work via automobile will switch to public transportation, and 70% will continue to commute via automobile. At the same time, it is expected that 20% of those now using public transportation will commute via automobile and 80% will continue to use public transportation. (a) Construct the transition matrix for the Markov chain that describes the change in the mode of transportation used by these commuters. P A T = P A (b) Find the initial distribution vector for this Markov chain. X0 = (c) What percentage of the commuters are expected to use public transportation 6 months…

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