(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.00048 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0002 x 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 mean standard deviation 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878
(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.) 0.00048 0.0005 Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.) 0.0002 x 0.0005 (d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.) 1.2 X 1.1 mean standard deviation 0.539 X 0.111 (e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.) 896.4426 X 0.878
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
Related questions
Question
100%
I need help with parts “c”, “d, and “e” thanks.

Transcribed Image Text:"Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a fixed point and the instant that the next car begins to pass that point. Let X = the time headway for two randomly chosen consecutive cars on a freeway during a period of heavy flow (sec). Suppose that in a
particular traffic environment, the distribution of time headway has the following form.
0
xs1
(a) Determine the value of k for which f(x) is a legitimate pdf.
11✔
11
(b) Obtain the cumulative distribution function.
F(x) =
x>1
0
mean
(c) Use the cdf from (b) to determine the probability that headway exceeds 2 sec. (Round your answer to four decimal places.)
0.0005
0.00048✔✔
Use the cdf from (b) to determine the probability that headway is between 2 and 3 sec. (Round your answer to four decimal places.)
0.0005
0.0002 x
standard deviation
x>1
(d) Obtain the mean value of headway and the standard deviation of headway. (Round your standard deviation to three decimal places.)
1.2 X
1.1
xs1
0.539 X
0.111
(e) What is the probability that headway is within 1 standard deviation of the mean value? (Round your answer to three decimal places.)
896.4426 X
0.878
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps

Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning

Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning

Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning


College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
