Jobs are sent to a printer at the average rate of 2 jobs per

Jobs are sent to a printer at the average rate of 2 jobs per minute. Binomial counting process is used to model these jobs. (a) What frame length gives the probability 0.1 of an arrival during any given frame? (b) With this value of , compute the expectation and standard deviation for the number of jobs sent to the printer during a 1-hour period. (c) Find the probability of more than 150 jobs sent to the printer during the next hour.

Solution

Given , average rate = 2 jobs per minute

60 sec = 2 jobs; 1 sec = 2/60 jobs

in 3 secs = 2*3/60 =0.1

The frame length= 3 sec or 3/60 =0.05min

b) Probability of one job = 0.1

in one hour , expected number of jobs sent to the printer = (3600/3)*0.1=120 jobs

standard deviation = sqrt(120*0.9)=10.39 jobs

c)P(X>150) =P(Z>(150.5-120)/10.39) = 0.001