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To monitor its water quality, a town plans to purchase several electronic sensors that will measure the degree of lead concentration in the water. Let c denote the true, but unknown, concentration of lead in the water (with units of parts per billion). No sensor is perfect, however, and so the town plans to average the results of multiple sensor readings S₁, S₂,..., Sy to come up with an estimate of the lead concentration: ➤Si. c= Two types of sensors are currently on the market: • Type A sensors have an error that follows a continuous uniform distribution between [-6, 6] parts per billion. The error is independent from one sensor to the next. Each Type A sensor costs $100. • Type B sensors have an error that follows a continuous Gaussian distribution with zero mean and standard deviation o = 2 parts per billion. The error is independent from one sensor to the next. Each Type B sensor costs $500. The town wishes to ensure that the estimate ê is accurate to within ±1 part per billion with probability at least 0.95. (a) How many Type A sensors would be required to achieve this level of accuracy? What would be the cost? (b) How many Type B sensors would be required to achieve this level of accuracy? What would be the cost?

To monitor its water quality, a town plans to purchase several electronic sensors that will measure the degree of lead concentration in the water. Let c denote the true, but unknown, concentration of lead in the water (with units of parts per billion). No sensor is perfect, however, and so the town plans to average the results of multiple sensor readings S₁, S₂,..., Sy to come up with an estimate of the lead concentration: ➤Si. c= Two types of sensors are currently on the market: • Type A sensors have an error that follows a continuous uniform distribution between [-6, 6] parts per billion. The error is independent from one sensor to the next. Each Type A sensor costs $100. • Type B sensors have an error that follows a continuous Gaussian distribution with zero mean and standard deviation o = 2 parts per billion. The error is independent from one sensor to the next. Each Type B sensor costs $500. The town wishes to ensure that the estimate ê is accurate to within ±1 part per billion with probability at least 0.95. (a) How many Type A sensors would be required to achieve this level of accuracy? What would be the cost? (b) How many Type B sensors would be required to achieve this level of accuracy? What would be the cost?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.6: Rational Functions
Problem 11SC: Find the mean hourly cost when the cell phone described above is used for 240 minutes.
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To monitor its water quality, a town plans to purchase several electronic sensors that will measure the degree of lead concentration in the water. Let c denote the true, but unknown, concentration of lead in the water (with units of parts per billion). No sensor is perfect, however, and so the town plans to average the results of multiple sensor readings S₁, S2,..., SN to come up with an estimate of the lead concentration: c= N i=1 Si. Two types of sensors are currently on the market: Type A sensors have an error that follows a continuous uniform distribution between [-6, 6] parts per billion. The error is independent from one sensor to the next. Each Type A sensor costs $100. • Type B sensors have an error that follows a continuous Gaussian distribution with zero mean and standard deviation o = 2 parts per billion. The error is independent from one sensor to the next. Each Type B sensor costs $500. The town wishes to ensure that the estimate ĉis accurate to within ±1 part per billion with probability at least 0.95. (a) How many Type A sensors would be required to achieve this level of accuracy? What would be the cost? (b) How many Type B sensors would be required to achieve this level of accuracy? What would be the cost?
Transcribed Image Text:To monitor its water quality, a town plans to purchase several electronic sensors that will measure the degree of lead concentration in the water. Let c denote the true, but unknown, concentration of lead in the water (with units of parts per billion). No sensor is perfect, however, and so the town plans to average the results of multiple sensor readings S₁, S2,..., SN to come up with an estimate of the lead concentration: c= N i=1 Si. Two types of sensors are currently on the market: Type A sensors have an error that follows a continuous uniform distribution between [-6, 6] parts per billion. The error is independent from one sensor to the next. Each Type A sensor costs $100. • Type B sensors have an error that follows a continuous Gaussian distribution with zero mean and standard deviation o = 2 parts per billion. The error is independent from one sensor to the next. Each Type B sensor costs $500. The town wishes to ensure that the estimate ĉis accurate to within ±1 part per billion with probability at least 0.95. (a) How many Type A sensors would be required to achieve this level of accuracy? What would be the cost? (b) How many Type B sensors would be required to achieve this level of accuracy? What would be the cost?
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