# Normal distribution assumption

1. Apr 10, 2012

### luckyluke

Hi everybody.
For sake of work I have to make an assumption that service time for patients is normally distributed.
Normally the doctor has to wait one patient every half hour but anyway this time can vary being less or more.
My teacher wants some theory arguments (normal distribution properties)why we can use normal distribution for modeling service time in our case.
This has to be in generally judging about process without looking on 3sigma,histogram etc.
I don't really know what to say
THX

2. Apr 10, 2012

### BWV

well the exponential distribution is usually used for waiting time problems, not the normal

unlike the normal, the waiting time cannot be negative

3. Apr 10, 2012

### luckyluke

Thank you.
It is about service time and there are many examples online where service time follow normal distribution...
For example
cob.jmu.edu/wangpx/kj/MS/5Sim/LectureSimHandout.pdf

where ATM service times follow normal distribution.
or
cs.mwsu.edu/~ranette/CMPS4223-Sim/Statistical%20Distr.ppt
where bus interarrival times are normally distributed.

Regards

4. Apr 10, 2012

### BWV

service time, waiting time have the same issues. just show that the variation in service time is more or less evenly distributed around the mean, without large outlier and the normal will work. Ideally subtracting 2-3 standard deviations from the mean does not get you a negative number. I.e. if the average service time is 1 minute but the SD is 10 minutes due to some large positive outliers then normal will not work. But if its 10 minutes with a standard deviation of 2 minutes normal is OK

5. Apr 10, 2012

### Stephen Tashi

A sum of identically distributed independent random variables is approximately normally distributed. I think there are some results relating the sum of independent non-identically distributed random variables to a normal distribution, but I can't quote them. If you think of the service of a patient as involving a sequence of many independent tasks (e.g. weighing the patient involves, walking to the scale, stepping on the scale, reading the scale, recording the weight) you could argue that a normal distribution approximates the sum of the elapsed times of these tasks.

6. Apr 15, 2012