Question
In: Statistics and Probability
Jobs are sent to a printer at an average rate of 6 jobs per hour. (a)...
Jobs are sent to a printer at an average rate of 6 jobs per hour.
(a) What is the expected time between jobs? [Note: Give the exact answer either in hours or in minutes.]
(b) What is the probability that the next job is sent within 4 minutes? [Note: Round the answer to four decimal places.]
Solutions
Expert Solution
Answer:
Given that,
Jobs are sent to a printer at an average rate of 6 jobs per
hour.
(a).
What is the expected time between jobs:
It is given that, jobs to a printer are sent at a rate of 6 jobs
per hour.
That is,
Since, the numbers of jobs sent to a printer follow Poisson
distribution, the time between jobs has an exponential
distribution.
The required mean time between successive jobs is,
=(Time Period)/(Number of complaints)
=60/6
=10
Thus, the expected time between successive jobs is 10 minutes.
In exponential distribution, 
is the rate parameter which is the inverse of the mean.
The required rate parameter is,
=1/10
=0.1
Thus, the rate parameter ()
of the exponential distribution is 0.1.
(b).
What is the probability that the next job is sent within 4 minutes:
The cumulative distribution function of Exponential distribution
is,
The probability that the next job will be sent within 4 minutes is
P(X 
4).
=1-0.6703
=0.3297
Thus, the probability that the next job will be sent within 4 minutes is 0.3297.
orchestra answered 1 year agoRelated Solutions
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