1. The daily flow rate of contaminant from an industrial plant is modeled by a normal random variable with a mean value of 10 units and a c.o.v. of 20%. When the contaminant flow exceeds 14 units on a given day, it is considered excessive. Assume that the contaminant flow rate between any 2 days is statistically independent.
a) What is the probability that the contaminant flow rate is excessive on any given day?
i. Identify the variable of interest and its distribution including the parameters.
ii. Now find the probability asked for in part a.
b) Regulation requires the measurement of contaminant flow rate for 3 days. The plant will be charged with a violation if excessive contaminant flow rate is observed during the 3-day period.
i. Identify the variable of interest and its distribution including the parameters.
Hint 1: It is not the same as in part a.
Hint 2: You aren't looking at the flow rate. Rather, you are looking at whether or not the flow rate is excessive. What type of situation is that?
ii. Now find the probability the company will not get a violation.
c) To decrease the risk of a violation, the company has decided to keep the probability of excessive contaminant flow at 0.0033 (or less). The plant cannot reduce the standard deviation of the contaminant flow rate, but can reduce the mean daily contaminant flow rate by improving the chemical process.
i. Identify the variable of interest and its distribution including the parameters.
ii. To meet this new policy, what should be the daily mean contaminant overflow rate?
d) Suppose the flow of contaminant can better be described by a lognormal distribution with a mean of 10 units and c.o.v. of 20%.
i. Identify the variable of interest and its distribution including the parameters.
ii. Is the probability of having excessive contaminant on any given day greater or smaller in this?