Call response time distribution [Help needed]

#1
Hello everyone!

I'm new to this forum but I want to start off by making a request.
The thing is I'm working on a project regarding call-back advertising and want to make a statistical model describing call response time.

Let's say that I've got 5000 subscribers to my service which receive on average 4 calls per day and that the average call response time is 7 seconds.

Now let's say that the advertiser is due to pay the following amount after:

5 sec - $.01
10 sec - $.02
15 sec - $.03
25 sec - $.05

That is, if an ad is played for 5 seconds, he will pay $.01, if 10 seconds pass he will pay $.02 etc.

How would one go about figuring out how many of the advertisements per year are in the 0-5 sec criterion, the 5-10 sec etc. and calculate the possible profit of said advertisements.

I've been trying to do the calculations for the response time with a Normal pdf with mean 7 seconds and standard deviations ranging from 2-5 seconds but I don't find the results believable.

Any advice on the problem is greatly appreciated!

Sincerely,
The Chosen One
 

BGM

TS Contributor
#2
What data did you have? It would be best if you have the raw data of counts in each criterion. In such case you can use the sample proportion as the estimator.
 
#3
What data did you have? It would be best if you have the raw data of counts in each criterion. In such case you can use the sample proportion as the estimator.
The thing is I don't have any raw data, only a vague reference that average response time is around 6-8 sec. and I wanted to use some distribution to make an estimated model.

Some kind of z-distribution might be the way to go.
 

BGM

TS Contributor
#5
You may start with exponential distribution with the desired mean. Since you did not have the raw data, nor have a strong assumption made, any positive distribution may fit your need.

If you want to use a distribution like normal, you need to use the truncated normal instead, as the support of ordinary normal distribution is including the negative real numbers.