# What is the average number of students waiting in line

For this Question, am having a problem determining the average number of students in the queue. My problem arises since by using the formula, am getting a decimal answer less than 1. The formula I used is $Lq$= $p^2$/$(1-p)$ where p is the probability that someone is being served. Thus I have $10/20$ =$0.5$. Computing for $Lq$ I got 0.5 which I believe is incorrect since we cannot have an average of 0.5 students on a queue. Where am I getting it wrong?

The students patiently form a single line in front of the desk to wait for help at State University has a help desk. Student arrivals are best described using a Poisson distribution with mean 10 students per hour arrive at the help desk. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system:

(a) The average number of students in the system
(b) The average number of students waiting in line

• You may want to read this and add the self-study tag. – Ian_Fin Nov 2 '16 at 9:29
• To add some general help: suppose that half the time there is one student in line and half the time there is no student in line, what is the average amount of students in line? – dimpol Nov 2 '16 at 9:33