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
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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![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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