Average response time
tl:dr--Anything between once a day and three times a week seems to be pretty common, as far as expected posting rates. Mileage may vary--
It's hard to establish an 'average' response time. I'm in a game now (have been for over a decade) where I typically post one or two times a day. Sometimes circumstances allow for more than that, but it's the exception, rather than the rule. There are times I'll log into the game and discover that the four or five active players (some with multiple characters) have racked up 30-50 posts in my absence...two or three of them happened to have some time available at the same time and got started rapid-firing posts back and forth. More commonly, most people are posting maybe three posts/day, between their characters, and it's not uncommon for Real Life to rear its ugly head and take some of us out of game circulation for days or even weeks at a time. There are one or two players who've had RL issues take them away from the game, but they stay in regular contact with the GM (they don't have time to post in-game, but they can squeeze in a quick PM every so often to let the GM know they're still alive and still interested in coming back to the game when personal circumstances allow). One guy may not post anything for weeks at a time, and then he'll show up and fire off ten or twelve posts and then he disappears again. "Average" is a hollow concept in those circumstances.
As others have said, decide how often YOU, as GM, want them to post. I've seen some who want daily posts (a few want multiple posts every day, but that's a big ask). Some want a few posts every week, some are happy with one post every week, and some are good with 'post when you can, and we'll make it work'. The more successful GMs I've played with will keep the plot moving and maintain their own desired posting rate (if they say "at least one post per day", they will update the game daily, at least, and sometimes more often if circumstances allow and the in-game situation calls for it.) But it's also important to have communication with your players, and to show understanding when circumstances confound your desired posting schedule. The GM running that decade-plus game I mentioned would have had the game go belly-up a long time ago if he ruthlessly cut everyone who failed to post as often as he asked them to (I'm his only player left from the starting lineup, and I'd have been bounced years ago...work typically gets crazy enough a few times each year that I basically show up and say, "Hey, it's tech and dress rehearsal season, I'll be reading but I won't have time to post anything for the rest of the month...") You want to stick to that posting rate, yes...but you've also got to exercise some understanding for your players' situations, as well, if you want to keep good players around.
There are a lot of other factors that can come into play, as well. Chemistry is the great intangible for gaming, especially PBP. If players mesh well with you and the other players, they can't wait to get back to the game and post again. If they like you but don't like some of the other players, they may go in fits and starts of rapid-fire posting interspersed with periods of minimal posting. (If they don't like you, hopefully they have the good sense to go find a game with a GM they like, because I can't imagine anything enjoyable about trying to keep posting in a game with a GM whose vibe just doesn't gel with mine...the game becomes a chore for both player and GM, at that point.) Posting styles...are you more descriptive? Dialogue-focused? Action-focused? Your players take cues from you and if you're using a style they favor, they're apt to be more responsive. There's...yeah. A LOT of variables...find what works for you, run with that, and let the players who don't jive with that filter themselves out. If a player's not having fun, it might slow the game down a bit...but if the GM's not having fun, it's not like there's four other GMs who can fill in the gaps (in most games, anyway...)