Question # 2. Suppose that at a particular air quality monitoring station, the monitoring devices system installed in the station are established to measure the level of the air pollution. The system will signal if the level of air pollution exceeds the allowable levels and will not signal if the levels are within acceptable ranges. The devices system signals with probability of 0.95 if allowable levels exceeded in a particular day and with probability of 0.005 if the air pollution levels are normal (below the allowable level) in a given day. The probability of occurrence of days in which the level exceeds the allowable level is 0.005. (a) What is the probability that the monitoring system will signal? (b) Estimate the probability that the air pollution level is normal given that the monitoring system signals.
Question # 2. Suppose that at a particular air quality monitoring station, the monitoring devices system installed in the station are established to measure the level of the air pollution. The system will signal if the level of air pollution exceeds the allowable levels and will not signal if the levels are within acceptable ranges. The devices system signals with probability of 0.95 if allowable levels exceeded in a particular day and with probability of 0.005 if the air pollution levels are normal (below the allowable level) in a given day. The probability of occurrence of days in which the level exceeds the allowable level is 0.005. (a) What is the probability that the monitoring system will signal? (b) Estimate the probability that the air pollution level is normal given that the monitoring system signals.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Question # 2.
Suppose that at a particular air quality monitoring station, the monitoring devices system
installed in the station are established to measure the level of the air pollution. The
system will signal if the level of air pollution exceeds the allowable levels and will not
signal if the levels are within acceptable ranges. The devices system signals with
probability of 0.95 if allowable levels exceeded in a particular day and with probability of
0.005 if the air pollution levels are normal (below the allowable level) in a given day. The
probability of occurrence of days in which the level exceeds the allowable level is 0.005.
(a) What is the probability that the monitoring system will signal?
(b) Estimate the probability that the air pollution level is normal given that the
monitoring system signals.
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