What bounce rate is still normal?

There is no official standard, but there are thresholds above which mail providers grow suspicious.

For a maintained list

Regular sending to a list you clean should stay well under one per cent. Above that, something is wrong in your process.

For a first send

An old list never cleaned can reach several per cent. That is expected, but it means you should have cleaned before sending.

The dangerous threshold

From a few per cent hard bounces you risk a block. Some providers stop the send mid-campaign.

Look at the distribution

An acceptable overall rate can hide one domain where everything bounces. That is a block, not dead addresses.

What to do

Validate on entry, remove hard bounces immediately, and clean before a big campaign rather than after.