Suppose that, from a survey of construction labor, the work duration (in number of hours) per day and the average productivity (in terms of efficiency) are obtained as follows: Duration (in hrs) Productivity Number of observations 5 50 4 5 60 1 5 80 15 7 50 13 7 60 22 7 80 11 50 46 60 14 80 11 50 6 11 60 11 80 11 (a) According to above table, calculate the joint distribution of work duration and productivity? (b) What is the marginal distribution of work duration? (c) What is the average working duration in a day? What is the standard deviation?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.EA: Extended Application Using Extrapolation To Predict Life Expectancy
Problem 6EA
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Suppose that, from a survey of construction labor, the work duration (in number of hours)
per day and the average productivity (in terms of efficiency) are obtained as follows:
Duration (in hrs) Productivity
Number of observations
5
50
4
5
60
11
5
80
15
7
50
13
7
60
22
7
80
11
9
50
46
9
60
14
80
8
11
50
11
60
9
11
80
11
(a) According to above table, calculate the joint distribution of work duration and
productivity?
(b) What is the marginal distribution of work duration?
(c) What is the average working duration in a day? What is the standard deviation?
(d) What is the correlation between work duration and productivity? Comment on this
value.
(e) If the work duration is 10 for a construction firm, what is the expected productivity?
What is its standard deviation?
Transcribed Image Text:Suppose that, from a survey of construction labor, the work duration (in number of hours) per day and the average productivity (in terms of efficiency) are obtained as follows: Duration (in hrs) Productivity Number of observations 5 50 4 5 60 11 5 80 15 7 50 13 7 60 22 7 80 11 9 50 46 9 60 14 80 8 11 50 11 60 9 11 80 11 (a) According to above table, calculate the joint distribution of work duration and productivity? (b) What is the marginal distribution of work duration? (c) What is the average working duration in a day? What is the standard deviation? (d) What is the correlation between work duration and productivity? Comment on this value. (e) If the work duration is 10 for a construction firm, what is the expected productivity? What is its standard deviation?
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