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 th measurement error X of a certain physical quantity is decided by the density function given below. Complete par through (c). 100 = (x(4-x²). f(x) k(4-x²), -15x51 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 i 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 th measurement error X of a certain physical quantity is decided by the density function given below. Complete par through (c). 100 = (x(4-x²). f(x) k(4-x²), -15x51 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 i probability this occurs? The probability is 0.220. (Type an integer or decimal rounded to three decimal places as needed.)
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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).
[k(4-x²).
f(x)=
/*(4-
-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
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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![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).
[k(4-x²).
f(x)=
/*(4-
-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
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.)](https://content.bartleby.com/qna-images/question/8c91d588-82d3-4c7c-9d54-a7a9f1f611d3/e235cbb6-232a-42ba-a730-13c0d1dd6a51/2o0fyt6_processed.png)
