The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35. (a) Determine the pdf of X. f(x) = 0 Sketch the corresponding density curve. f(x) 0.20 0.15 0.10 0.05 f(x) 0.20 0.15 0.10 0.05 ≤ X ≤ otherwise 25 30 35 25 30 35 (b) What is the probability that preparation time exceeds 33 min? f(x) 0.20 0.15 0.10- 0.05- f(x) 0.20 0.15- 0.10 0.05 x 25 30 35 x 25 30 35 (c) What is the probability that preparation time is within 4 min of the mean time? [Hint: Identify μ from the graph of f(x).] (d) For any a such that 25 < a
The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35. (a) Determine the pdf of X. f(x) = 0 Sketch the corresponding density curve. f(x) 0.20 0.15 0.10 0.05 f(x) 0.20 0.15 0.10 0.05 ≤ X ≤ otherwise 25 30 35 25 30 35 (b) What is the probability that preparation time exceeds 33 min? f(x) 0.20 0.15 0.10- 0.05- f(x) 0.20 0.15- 0.10 0.05 x 25 30 35 x 25 30 35 (c) What is the probability that preparation time is within 4 min of the mean time? [Hint: Identify μ from the graph of f(x).] (d) For any a such that 25 < a
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 4ECP
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![The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35.
(a) Determine the pdf of X.
f(x) =
0
Sketch the corresponding density curve.
f(x)
0.20
0.15
0.10
0.05
f(x)
0.20
0.15
0.10
0.05
≤ X ≤
otherwise
25
30
35
25
30
35
(b) What is the probability that preparation time exceeds 33 min?
f(x)
0.20
0.15
0.10-
0.05-
f(x)
0.20
0.15-
0.10
0.05
x
25
30
35
x
25
30
35
(c) What is the probability that preparation time is within 4 min of the mean time? [Hint: Identify μ from the graph of f(x).]
(d) For any a such that 25 < a <a + 4 < 35, what is the probability that preparation time is between a and a + 4 min?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa93602ec-ddf4-4381-b459-7694245b5f33%2Fdb7f9722-4589-43f0-b732-cb64129b921b%2Fj5ldvww_processed.png&w=3840&q=75)
Transcribed Image Text:The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35.
(a) Determine the pdf of X.
f(x) =
0
Sketch the corresponding density curve.
f(x)
0.20
0.15
0.10
0.05
f(x)
0.20
0.15
0.10
0.05
≤ X ≤
otherwise
25
30
35
25
30
35
(b) What is the probability that preparation time exceeds 33 min?
f(x)
0.20
0.15
0.10-
0.05-
f(x)
0.20
0.15-
0.10
0.05
x
25
30
35
x
25
30
35
(c) What is the probability that preparation time is within 4 min of the mean time? [Hint: Identify μ from the graph of f(x).]
(d) For any a such that 25 < a <a + 4 < 35, what is the probability that preparation time is between a and a + 4 min?
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