Every year, all oil companies that operate production fields on the Norwegian continental shelfmust report pollutant emissions to air and sea to the Norwegian Petroleum Directorate and theNorwegian Pollution Control Board. Beneath most reservoirs there is a zone of water which, aftersome time of production, is drawn up into the wells and becomes part of the "liquid" produced inthe fields. The water is separated from the oil, but some oil remains in this production water.Based on current technology, it can be assumed that the oil concentrations in randomly selecteddischarges of production water released into the sea are normally distributed with expectation μ= 21.6 mg/l and standard deviation o = 3.4 mg/l.The authorities require that the oil concentration in production water released into the sea mustbe less than 30 mg/l.a) Find the probability that a randomly selected emission exceeds the authorities'requirements.b) What is the probability that a randomly selected discharge is less than 25 mg/l?c) Find the probability that the oil concentration in production water in a randomly selecteddischarge will lie within [µ - 3o, µ + 30].

GivenMean(μ)=21.6standard deviation(σ)=3.4The authorities require that the oil concentration in…

Answered: Every year, all oil companies that…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A new analytical method to detect pollutants (D) in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants-organic pollutants (O), volatile solvents (V), and chlorinated compounds (C)-instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated components with 89.7% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated compounds. A test sample is selected randomly. (a) What is the probability that the test will signal? (b) If the test signals, what is the probability that chlorinated compounds are present? Note: Use the notations in the brackets to…
Casper Geriatric Center, a senior medical facility located in a large hospital in New Zealand, started a procedure where their guests receive their meals in their rooms while the food is still as hot as possible. The facility will continue to prepare the food in the commissary, but will now deliver it in bulk (not individual servings) to one of three new meal serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and sections of the facility. The three new serving stations are as efficiently located as possible to reach the various hallways in the faility. The purpose of the new procedure is to increase the temperature of the hot meals that the guest receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to section. The table below summarizes the time associated with…
There are three types of contaminants that spoils water. Organic pollutants (0), volatile solvents (V), and chlorinated compounds (C). A new analytical method to detect (D) contaminants in water is being tested. The makers of the test claim that it can detect high levels of organic pollutants with 98% accuracy, volatile solvents with 99% accuracy, and chlorinated components with 89% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated compounds. A test sample is selected randomly. (a) What is the probability that the test will not signal? (b) If the test signals, what is the probability that chlorinated compounds are present? (c) If the test does not signal, what is the probability that chlorinated compounds are present? Note: Use the notations in the brackets to describe the events.
Casper Geriatric Center, a senior medical facility located in a large hospital in New Zealand, started a procedure where their guests receive their meals in their rooms while the food is still as hot as possible. The facility will continue to prepare the food in the commissary, but will now deliver it in bulk (not individual servings) to one of three new meal serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and sections of the facility. The three new serving stations are as efficiently located. possible to reach the various hallways in the facility. The purpose of the new procedure is to increase the temperature of the hot meals that the guest receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to section. The table below summarizes the time associated with each…
In the production process of a company, 4 units of a certain input are used daily. It happens that the different formulations of this input can affect the yield of the process as well as the level of environmental pollution. On a given day the company has 40 units of this input in stock and they can be classified according to the table below:
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The dams in and around Cape Town form part of the Western Cape Water Supply System, which is an integrated and collectively managed system of dams, pump stations, pipelines, and tunnels. In addition to servicing Cape Town, the system supplies water to towns in the Overberg, Boland, West Coast, and Swartland areas, and provides irrigation water for agriculture. The change in depth of the Steenbras dam from one day to the next, measured (in feet) at in Cape Town, is a random variable Y with the following density function: f(y) = 2 < y< 4, elsewhere. 2.4.1. Define the random variable Y. 2.4.2 State what type of distribution does Y follow and why: 2.4.3. Find E (Y) and interpret your answer.
Assume that producing 1 unit of calcium requires 0.4 units of calcium, 0.1 units of hydrogen, and 0.1 units of sea salt; that producing 1 nit of hydrogen requires 0.2 units of calcium, 0.3 units of hydrogen, and 0.1 units of sea salt; and that producing 1 unit of sea salt equires 3 units of calcium, 0 units of hydrogen, and 0.2 units of sea salt. Find the production schedule that satisfies an external demand for 41 units of calcium, 39 units of hydrogen, and 11 units of sea salt. X =
It is often said that the economy of Arizona depends on the “Five C’s”: Copper, Cattle, Cotton, Citrus, andClimate. Assume a (highly simplified) model of the Arizona Economy that depends only on C1, C2, C3, C4,and C5, which represent the number of economic units (pennies, pounds, etc) purchased of each of the FiveC’s, respectively. Further assume that the Utility, or Economic Value (which is different from DollarValue), can be described by the function:U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond tothe minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Cimake sense from an economic standpoint?

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