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Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). f(x)=√k(4-x²), -1≤x≤1 elsewhere (a) Determine k that renders f(x) a valid density function. 3 k= (Type an integer or a simplified fraction.) 22 2 (b) Find the probability that a random error in measurement is less than 3 The probability is 0.850 (Type an integer or decimal rounded to three decimal places as needed.) (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., Ixl) exceeds 0.75. What is the probability this occurs? The probability is 0.220 (Type an integer or decimal rounded to three decimal places as needed.)

Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). f(x)=√k(4-x²), -1≤x≤1 elsewhere (a) Determine k that renders f(x) a valid density function. 3 k= (Type an integer or a simplified fraction.) 22 2 (b) Find the probability that a random error in measurement is less than 3 The probability is 0.850 (Type an integer or decimal rounded to three decimal places as needed.) (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., Ixl) exceeds 0.75. What is the probability this occurs? The probability is 0.220 (Type an integer or decimal rounded to three decimal places as needed.)

A First Course in Probability (10th Edition)
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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Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). f(x)= k(4-x²). { -1≤x≤1 elsewhere (a) Determine k that renders f(x) a valid density function. 3 k= (Type an integer or a simplified fraction.) 22 2 (b) Find the probability that a random error in measurement is less than 3 The probability is 0.850 (Type an integer or decimal rounded to three decimal places as needed.) (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., x)) exceeds 0.75. What is the probability this occurs? The probability is 0.220 (Type an integer or decimal rounded to three decimal places as needed.)
Transcribed Image Text:Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a) through (c). f(x)= k(4-x²). { -1≤x≤1 elsewhere (a) Determine k that renders f(x) a valid density function. 3 k= (Type an integer or a simplified fraction.) 22 2 (b) Find the probability that a random error in measurement is less than 3 The probability is 0.850 (Type an integer or decimal rounded to three decimal places as needed.) (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., x)) exceeds 0.75. What is the probability this occurs? The probability is 0.220 (Type an integer or decimal rounded to three decimal places as needed.)
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