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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