Question 1121571: A university IT department uses a statistical model to help to determine how much student printing capacity to provide. The model assumes that print jobs arrive in a print queue at random and independently. The model also assumes that the average number of print jobs arriving per hour is 150.
Decide what kind of distribution is being used to model the number of print jobs arriving in an interval of time and use this to find the probability of less than 5 print jobs arriving in a one minute interval.
Enter your answer, correct to 3 decimal places
Thanks in advance
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! This is a Poisson distribution with variables random, independent, proportional to time, theoretically independent number in a time interval.
per minute there are 2.5 print jobs, and that is lambda, the Poisson parameter.
fewer than 5 print jobs is 0,1,2,3,4
can do by hand or table
by hand e^(-2.5)2.5^0/0! is for 0=0.082 from e^(-lambda)*lambda^x/x!
e^(-2.5)*2.5/1!=0.205 for 1
e^(-2.5)*2.5^2/2=0.257
e^(-2.5)*2.5^3/6=0.214
e^(-2.5)*2.5^4/24=0.134 for 4
0.891 is the probability if rounding occurs at the end (0.892 if the rounding occurs to 3 decimal places and those are added).
0.891 ia the probability from the table
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