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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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