Wallace Publishers has a large number of employees who use the company’s single fax machine. Employees arrive ran-domly to use the fax machine at an average rate of 20 per hour. This arrival process is approximated by a Poisson distri-bution. Employees spend an average of two minutes using the fax machine, either transmitting or receiving items. Thetime spent using the machine is distributed according to anegative exponential distribution. Employees line up in single file to use the machine, and they obtain access to it on a first-come, first-served basis. There is no defined limit to the number who can line up to use the machine. Management has determined that by assigning an oper-ator to the fax machine rather than allowing the employees to operate the machine themselves, it can reduce the aver-age service time from the current 2 minutes to 1.5 minutes. However, the fax operator’s salary is $8 per hour, which must be paid 8 hours per day even if there are no employ-ees wishing to use the fax machine part of the time. Man-agement has estimated the cost of employee time spent waiting in line and at the fax machine during service to be17¢ per minute (based on an average salary of $10.20 perhour per employee). Should the firm assign an operator tothe fax machine?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Wallace Publishers has a large number of employees who use
the company’s single fax machine. Employees arrive ran-
domly to use the fax machine at an average rate of 20 per
hour. This arrival process is approximated by a Poisson distri-
bution. Employees spend an average of two minutes using
the fax machine, either transmitting or receiving items. The
time spent using the machine is distributed according to a
negative exponential distribution. Employees line up in single
file to use the machine, and they obtain access to it on a first-
come, first-served basis. There is no defined limit to the
number who can line up to use the machine.
Management has determined that by assigning an oper-
ator to the fax machine rather than allowing the employees
to operate the machine themselves, it can reduce the aver-
age service time from the current 2 minutes to 1.5 minutes.
However, the fax operator’s salary is $8 per hour, which
must be paid 8 hours per day even if there are no employ-
ees wishing to use the fax machine part of the time. Man-
agement has estimated the cost of employee time spent
waiting in line and at the fax machine during service to be
17¢ per minute (based on an average salary of $10.20 per
hour per employee). Should the firm assign an operator to
the fax machine?
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