Question

An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with u = 0.40 and 0 = 0.08. (Round your answers to four decimal places.) (a) What is the probability that the concentration exceeds 0.60? (b) What is the probability that the concentration is at most 0.30? (c) How would you characterize the largest 5% of all concentration values? The largest 5% of all concentration values are above mg/cm3 You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Solution Given that l = 0.40 6 = 0.08 a) p(x>0,60.) - - P(x- - 6' 0.60 -0.40 0.08 . - | - P ( z 2,5 ) = 1- 0.9938 - 0.00 62 Pao baki, y 0.0062

6) P ( x 20.30) |=P ( x-uc 0.30 - Ordo 5 0 .08 ) = P( 22 -0.1) = P(ac - 1.25) - 0.1056 probabinity = 0.1056

C) using standard normal table P(Z >z) : 54 1-P(ziz)= 0.05 PCZLZ) = 1-0.05 -0.95 PCZC 1.645)=0.95 Z = 1.645 using a score formula x = zote = 1.645 x 0,08 +0.40 x = 0.5316 The largest 5.7 of all concentration volves are above 0,5316 mg/cm