A construction company manages two large building projects. Both require about 50 employees with comparable skills. At a meeting, the site managers from the two projects got together to estimate the labor needs of their projects during the coming winter. At the end of the meeting, each manager provided a table that showed how they expected weather to impact their labor needs.

A subsequent discussion with experts at the National Weather Service indicated the following probabilities for the various types of winter weather.

Motivation
(a) Why should the company consult with these site managers about the labor needs of their project for the coming winter season?
(b) Is it more useful to have a probability distribution for the weather, or should management base its decisions on only the most likely form of winter weather (i.e., typical weather)?
Method
(c) Identify the key random variable for planning the labor needs of these two sites.
Mechanics
(d) Find the probability distribution for the number of labor employees needed at both sites.
(e) Find the expected total number of labor employees needed for both sites.
(f) Find the standard deviation of the total number of labor employees needed at both sites.
Message
(g) Summarize your findings for management. How many laborers do you think will be needed during the coming season? Are you sure about your calculation? Why or why not?

Site 1 Winter Conditions Mild Typical Cold Severe 100 Number of labor employees 70 40 20 Site 2: Winter Conditions Mild Typical Cold Severe Number of labor employees 80 50 40 30 Winter Conditions Mild Typical Cold Severe 0.30 0.40 0.200.10 Probability