CHAPTER 2-3

2.14

A construction job is comprised of two tasks, which we will call''task A\" and \"task B.\" The two tasks are initiated simultaneouslyand their completion times are uncertain. The entire constructionjob is completed as soon as both tasks are completed. The possibleoutcomes for the completion times of task A and task B, and theassociated probabilities, are given in Table 2.28.

TABLE 2.28 Probabilities of time to completion of tasks A andB. Time to Complete Task A (in weeks) Time to Complete Task B (in weeks) Probability 1 1 0.07 1 2 0.27 1 3 0.06 2 1 0.13 2 2 0.31 2 3 0.16

	(a) What is the probability distribution of the duration of taskA? of task B? of the job as a whole?

	(b) What is the mean and the standard deviation of the durationof task A? of task B? of the job as a whole?

	(c) Suppose that task A costs $800 for every week that it is inprogress, and that task B costs $1,000 per week for every week thatit is in progress, and that there is an additional charge of $400for every week that the job as a whole is still in progress.Compute the probability distribution, the mean, and the standarddeviation of the cost of this construction job.

Exercise 2.19

A package delivery company experiences high variability in dailycustomer demand, which in turn results in high variability in thedaily workload at the central sorting facility. The company relieson its sorting facility employees working overtime to provideon-time delivery when the workload demand is very high. A sortingfacility employee receives a salary of $12/hour for a 40 hour week,and the employee receives $18/hour for every hour worked overtime,that is, for every hour worked over 40 hours in a given week. Thenumber of overtime hours that an employee works in any given weekis a random variable, with a mean of 15 hours and a standarddeviation of 4 hours. What are the mean, the standard deviation,and the variance of an employee's total weekly salary?