The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. 1- 2≤x≤4 f(x) = ) = {* [¹ − (x − 3)²] 0 otherwise (a) Sketch the graph of f(x). f(x) f(x) 1.0 0.8 0.6 0.4 0.2 Xx 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 f(x) f(x) 1.0 1.0 0.8 0.8 hh 0.6 0.6 0.4 0.4 0.2 0.2 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 (b) Find the value of k. (c) What is the probability that the actual tracking weight is greater than the prescribed weight? (d) What is the probability that the actual weight is within 0.55 g of the prescribed weight? (Round your answer to four decimal places.) (e) What is the probability that the actual weight differs from the prescribed weight by more than 0.6 g? (Round your answer to four decimal places.) X 1.0 0.8 0.6 0.4 0.2
The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf. 1- 2≤x≤4 f(x) = ) = {* [¹ − (x − 3)²] 0 otherwise (a) Sketch the graph of f(x). f(x) f(x) 1.0 0.8 0.6 0.4 0.2 Xx 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 f(x) f(x) 1.0 1.0 0.8 0.8 hh 0.6 0.6 0.4 0.4 0.2 0.2 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 (b) Find the value of k. (c) What is the probability that the actual tracking weight is greater than the prescribed weight? (d) What is the probability that the actual weight is within 0.55 g of the prescribed weight? (Round your answer to four decimal places.) (e) What is the probability that the actual weight differs from the prescribed weight by more than 0.6 g? (Round your answer to four decimal places.) X 1.0 0.8 0.6 0.4 0.2
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter10: Radical Functions And Equations
Section: Chapter Questions
Problem 9CR
Related questions
Question
![The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.
|1 -
2≤x≤4
f(x) = {K[¹ − (x − 3)²]
0
otherwise
(a) Sketch the graph of f(x).
f(x)
f(x)
X
3.0
2.0 2.5
3.5 4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5
O
O
f(x)
f(x)
1.0
1.0
0.8
0.8
hh
0.6
0.6
0.4
0.4
0.2
0.2
+ X
X
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
4.5
3.0
3.5
4.0
O
(b) Find the value of k.
(c) What is the probability that the actual tracking weight is greater than the prescribed weight?
(d) What is the probability that the actual weight is within 0.55 g of the prescribed weight? (Round your answer to four decimal places.)
(e) What is the probability that the actual weight differs from the prescribed weight by more than 0.6 g? (Round your answer to four decimal places.)
1.0
0.8
0.6
0.4
0.2
X
1.0
0.8
0.6
0.4
0.2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d158991-3671-4459-aef6-bd0615668acc%2F04e4c31f-ee5f-4495-afd9-7d6b8ee39b11%2Fx5kpwaf_processed.png&w=3840&q=75)
Transcribed Image Text:The actual tracking weight of a stereo cartridge that is set to track at 3 g on a particular changer can be regarded as a continuous rv X with the following pdf.
|1 -
2≤x≤4
f(x) = {K[¹ − (x − 3)²]
0
otherwise
(a) Sketch the graph of f(x).
f(x)
f(x)
X
3.0
2.0 2.5
3.5 4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5
O
O
f(x)
f(x)
1.0
1.0
0.8
0.8
hh
0.6
0.6
0.4
0.4
0.2
0.2
+ X
X
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
4.5
3.0
3.5
4.0
O
(b) Find the value of k.
(c) What is the probability that the actual tracking weight is greater than the prescribed weight?
(d) What is the probability that the actual weight is within 0.55 g of the prescribed weight? (Round your answer to four decimal places.)
(e) What is the probability that the actual weight differs from the prescribed weight by more than 0.6 g? (Round your answer to four decimal places.)
1.0
0.8
0.6
0.4
0.2
X
1.0
0.8
0.6
0.4
0.2
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