Answer:
a) %idle time = 0.33
b)40.2minutes
c)40.02customers
d)0.5219
Step-by-step explanation:
It was said in the question Students arrive at the Administrative Services Office at an average of one every 15 minutes which means that
λ = 60/15= 4customers/hr
It was stated that their requests take on average 10 minutes to be processed which means that
μ = average of 10minutes = 60/10 = 6customers/hr
Then let us use these information to solve the given questions
a) percentage when judy was idle = (1- λ/μ)= 1- 0.67= 0.33
%service time = 0.67
%idle time = 0.33
b)To calculate How much time, on average that a student spend waiting in line then we make use of the formula below
= λ/ μ( μ- λ)
= 0.67hrs = 0.67 x60 = 40.2minutes
c) To calculate How long the waiting line on average;
= average waiting time x arrival rate = 0.67hrs x 6customers/hr
= 40.02customers
d) the probability that an arriving student will find at least one other student waiting in line is calculated below;
P( idle time i.e no customer to attend to) = 0.33
P1( Probability of having a customer to attend to) = 0.33 x 0.67= 0.2211
P( Probability of having 2 customer to attend to) = 0.33 x 0.67x0.67 = 0.1481
Therefore, the probability of finding at least one customer = 1 -[ po + p1]
= 1 - 0.33- 0.1481 = 0.5219
