1. The daily waste amount produced from a factory can be modeled with normal distribution with a mean value of = 12 units and a coefficient of variation of 8x = 0.15. When the waste amount exceeds 15 units on a given day,

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1. The daily waste amount produced from a factory can be modeled with normal distribution with a mean value of
Hx = 12 units and a coefficient of variation of 8x = 0.15. When the waste amount exceeds 15 units on a given day,
it is considered as “excessive" by regulating authority. Assume that the daily waste amount between any two days is
statistically independent.
a) What is the probability of having “excessive" waste amount on a given day?
b) Regulation requires the measurement of waste amount for 3 days. The factory will be charged with a violation
if excessive waste amount is observed during the 3-day period. What is the probability that the factory will
not be charged with violation?
c) Suppose that the factory cannot reduce the standard deviation of the daily waste amount, however it can reduce
the mean daily waste amount by improving the chemical process. If the factory decides to limit violation to
1.5%, what should be the daily mean value of the waste amount?
Transcribed Image Text:1. The daily waste amount produced from a factory can be modeled with normal distribution with a mean value of Hx = 12 units and a coefficient of variation of 8x = 0.15. When the waste amount exceeds 15 units on a given day, it is considered as “excessive" by regulating authority. Assume that the daily waste amount between any two days is statistically independent. a) What is the probability of having “excessive" waste amount on a given day? b) Regulation requires the measurement of waste amount for 3 days. The factory will be charged with a violation if excessive waste amount is observed during the 3-day period. What is the probability that the factory will not be charged with violation? c) Suppose that the factory cannot reduce the standard deviation of the daily waste amount, however it can reduce the mean daily waste amount by improving the chemical process. If the factory decides to limit violation to 1.5%, what should be the daily mean value of the waste amount?
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