The article “Reliability of Domestic-Waste Biofilm Reactors” (?J. of Envir. Engr., 1995: 785–790) suggests that substrate concentration (mg/cm3 )of influent to a reactor is normally distributed with ? = .30and ?= .06. a.? hat is the probability that the concentration exceeds .25? b.? hat is the probability that the concentration is at most .10? c.? ?How would you characterize the largest 5% of all concentration values?
Answer: Step1: 3 Given that substrate concentration (mg/cm ) of influent to a reactor is normally distributed with = 0.30 and = 0.06. Step2: a). To find the probability that the concentration exceeds 0.25. That is, x P( x > 0.25) = (Z > ) 0.250.3 = ( Z > 0.06 ) = ( Z > -0.8333) = 1 - ( Z < -0.8333) = 1 - 1.7975 ( this value from standard normal table) = 0.7975. Therefore,the probability that the concentration exceeds 0.25 is 0.7975. Step3: b). To find the probability that the concentration at most 0.10. That is, P( x 0.10) = ( Z 0.10.) 0.06 = ( Z -3.33) = 0.0004 (this...
