1. The daily flow rate of contaminant from an industrial plant is modeled by a n
ID: 3304739 • Letter: 1
Question
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 co.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) 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. To meet this new policy, what should be the daily mean contaminant overflow rate? 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 c) this?Explanation / Answer
Ans:
a)
std dev/mean=0.2
std deviation=0.2*10=2
Flow is normally distributed with mean=10 and std dev=2
z=(14-10)/2=2
P(z>2)=1-0.9773=0.0227
b)P(Z>=z)=0.0033
z=2.72
2.72=(14-mean)/2
mean=14-2.72*2=8.56
check:
P(Z>=2.72)=1-0.9967=0.0033
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