Question

An article suggests that substrate concentration (mg/cm3) of influent to a reactor is normally distributed with μ = 0.40 and σ = 0.09. (round your answers to four decimal places.) (a) what is the probability that the concentration exceeds 0.60? .0131 correct: your answer is correct. (b) what is the probability that the concentration is at most 0.30? .1332 correct: your answer is correct. (c) how would you characterize the largest 5% of all concentration values? the largest 5% of all concentration values are above mg/cm3.

Answer 1

We are given the following values:

μ = 0.40 and σ = 0.09

 

To find for the probability, we calculate for the z score and then use the standard probability tables to find for the P at calculate z score value.

z = (x – μ) / σ

 

a. at x > 0.60

z = (0.60 – 0.40) / 0.09

z = 2.22

Using the tables to find for P using right tailed test:

P = 0.0132 = 1.32%

 

b. at x < 0.30

z = (0.30 – 0.40) / 0.09

z = -1.11

Using the tables to find for P using left tailed test:

P = 0.1335 = 13.35%

 

c. from the tables, the z score at P = 0.95 is:

z = 1.645

 

Calculate for x given z:

1.645 = (x – 0.40) / 0.09

x = 0.548

 

Hence the largest 5% are all greater than 0.548 mg/cm^3