Send email about pending registration?

Is there a way to send and email or notify on the screen submission that user’s registration is pending? It goes through on my site as if they registered and then were already approved because it immediately sends them their login pw and username via email. The admin also just receives an email that says someone signed up and does not tell the admin to go in and approve them. If you log in and look at the user, they are in fact pending, but the notifications don’t correlate to any of that with this plugin – it just uses the defaults with wordpress user sign ups settings. I’d also like the user to get an email saying they’ve been approved when this occurs. If this isn’t possible, what plugin can achieve this?