what is a "normal" connection time?

I currently measure an average of 110ms for open the db connection. However, the number varies between 1 ms and 1000ms. The server has a load of about 500-1500 connections/s.
Now I’m trying to find out if the connection time is normal or there is a problem. Therefore the question => what are normal values or normal fluctuations with such a utilization?

Hi @Maik80

Please check below few things : 
1) how many max connections configured?
2) what is max thread cache?
3) are connections getting closed properly by application?
4) what is the concurrency during peak (when it goes to 1000ms)
5) is slow query log enabled ? if yes please analyse during peak (1000ms)

let me know you need any help to capture any of above. 
I highly recommend to use PMM Percona Monitoring and Management
to get better understanding and visibility of MySQL performance issues.