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For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________
Correct answer is '210'. Can you explain this answer?
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For a construction project. The mean and standard deviation of the com...
For 95% confidence level z = 1.64
TE = 200 days
σ = 6.1days
TS = TE + zσ = 200 + 1.64 × 6.1 = 200 + 10.004 = 210.004 days
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For a construction project. The mean and standard deviation of the com...
Mean and Standard Deviation
The mean completion time for the construction project is given as 200 days, and the standard deviation is 6.1 days. The mean represents the average time it takes to complete the project, while the standard deviation measures the variability or spread of completion times around the mean.
Assuming Normal Distribution
The assumption of a normal distribution allows us to use statistical techniques to estimate the probability of certain events occurring. In this case, we can use the normal distribution to estimate the probability of completing the project within a certain time frame.
Standard Normal Deviate (Z)
The standard normal deviate, also known as the z-score, is a measure of how many standard deviations a particular value is away from the mean. In this case, we are given a z-score of 1.64, which corresponds to the 95% confidence level. This means that there is a 95% probability that the completion time falls within 1.64 standard deviations of the mean.
Finding the Maximum Time
To find the maximum time required for the completion of the project, we need to determine the value that corresponds to a z-score of 1.64. This can be done by using the formula:
Maximum Time = Mean + (Z * Standard Deviation)
Substituting the given values into the formula, we have:
Maximum Time = 200 + (1.64 * 6.1) = 210.04
Interpreting the Result
The maximum time required for the completion of the project is calculated to be 210.04 days. However, since time is measured in whole numbers, we round down to the nearest whole number, which gives us a maximum time of 210 days.
This means that there is a 95% probability that the project will be completed within 210 days or less. The 95% confidence level indicates that if we were to repeat this project many times, we would expect 95% of the completion times to fall within this range.
Therefore, the correct answer is 210 days.
The mean completion time for the construction project is given as 200 days, and the standard deviation is 6.1 days. The mean represents the average time it takes to complete the project, while the standard deviation measures the variability or spread of completion times around the mean.
Assuming Normal Distribution
The assumption of a normal distribution allows us to use statistical techniques to estimate the probability of certain events occurring. In this case, we can use the normal distribution to estimate the probability of completing the project within a certain time frame.
Standard Normal Deviate (Z)
The standard normal deviate, also known as the z-score, is a measure of how many standard deviations a particular value is away from the mean. In this case, we are given a z-score of 1.64, which corresponds to the 95% confidence level. This means that there is a 95% probability that the completion time falls within 1.64 standard deviations of the mean.
Finding the Maximum Time
To find the maximum time required for the completion of the project, we need to determine the value that corresponds to a z-score of 1.64. This can be done by using the formula:
Maximum Time = Mean + (Z * Standard Deviation)
Substituting the given values into the formula, we have:
Maximum Time = 200 + (1.64 * 6.1) = 210.04
Interpreting the Result
The maximum time required for the completion of the project is calculated to be 210.04 days. However, since time is measured in whole numbers, we round down to the nearest whole number, which gives us a maximum time of 210 days.
This means that there is a 95% probability that the project will be completed within 210 days or less. The 95% confidence level indicates that if we were to repeat this project many times, we would expect 95% of the completion times to fall within this range.
Therefore, the correct answer is 210 days.
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For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer?
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For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer?.
For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a construction project. The mean and standard deviation of the completion time are 200 days and 6.1 days, respectively. Assume normal distribution and use the value of standard normal deviate Z = 1.64 for the 95% confidence level. The maximum time required (in days) for the completion of the project would be __________Correct answer is '210'. Can you explain this answer?.
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