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. f(x) = {^[1 · k1- (x- 0 2 ≤ x ≤ 4 otherwise (a) Sketch the graph of f(x). f(x) 1.0 0.8 О 0.6 0.4- 0.2 f(x) 1.0 0.8 0.6 0.4 0.2 - x 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. f(x) 1.0 0.8 0.6 0.4 0.2 f(x) 1.0 0.8 0.6 0.4 0.2 X 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 (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 0.45 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 0.5 g? (Round your answer to four decimal places.)
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. f(x) = {^[1 · k1- (x- 0 2 ≤ x ≤ 4 otherwise (a) Sketch the graph of f(x). f(x) 1.0 0.8 О 0.6 0.4- 0.2 f(x) 1.0 0.8 0.6 0.4 0.2 - x 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. f(x) 1.0 0.8 0.6 0.4 0.2 f(x) 1.0 0.8 0.6 0.4 0.2 X 2.0 2.5 3.0 3.5 4.0 4.5 2.0 2.5 3.0 3.5 4.0 4.5 (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 0.45 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 0.5 g? (Round your answer to four decimal places.)
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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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.
f(x)
= {^[1 ·
k1-
(x-
0
2 ≤ x ≤ 4
otherwise
(a) Sketch the graph of f(x).
f(x)
1.0
0.8
О
0.6
0.4-
0.2
f(x)
1.0
0.8
0.6
0.4
0.2
- x
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.
f(x)
1.0
0.8
0.6
0.4
0.2
f(x)
1.0
0.8
0.6
0.4
0.2
X
2.0
2.5
3.0
3.5
4.0
4.5
2.0
2.5
3.0
3.5
4.0
4.5
(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 0.45 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 0.5 g? (Round your answer to four decimal places.)
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