Question

An article suggests that substrate concentration (mg/cm³) of influent to a reactor is normally distributed with

μ = 0.30

and

σ = 0.08.

(Round your answers to four decimal places.)

(a)

What is the probability that the concentration exceeds 0.50?

(b)

What is the probability that the concentration is at most 0.20?

(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

μ = 0.30

and

σ = 0.08.

a) P(X > 0.50)

z = (0.50 - 0.30)/0.08 = 2.5

P(z > 2.5) = 0.0062

b) P(X ≤ 0.20)

z = (0.20 - 0.30)/0.08 = -1.25

P(z ≤ -1.25) = 0.1057

c) 1 - φ(z) = 0.05
φ(z) = 0.95
z = 1.645
X = 0.30 + 1.645 * 0.08 = 0.4316
The largest 5% of all concentration values are those above 0.4316