Firstly, Norton and 360 Security are different apps by 2 different companies. If you're trying to install something that claims to be "Norton 360", don't.
Secondly, you don't need anti-virus software on Android. In fact, your device is better without it.
There's only 2 ways to get malware on your device:
One is that you changed the security setting to allow app installation from "unknown sources" and downloaded something off a website or perhaps a "cracked" app/game from a torrent site. The file will have a .apk extension, and the device will ask if you want to install it. It'll also have a list of permissions you'd be granting it. That is, if you've already checked the "unknown sources" box, otherwise you'll get a message saying that you've chosen not to install apps from unknown sources. If you don't do this, then you have absolutely nothing to worry about. Unless...
You downloaded something from the Play Store that turns out to be malware. Google is extremely vigilant about security, especially keeping the Play Store free of malware and fake/clone apps, but nothing is 100%. Ironically, one of the more infamous instances of a malicious app being on Play was called "Virus Shield". How was "Virus Shield" discovered? I don't know, but it wasn't Norton or 360 or Avast or any other "anti-virus" app.
Just use your head. Don't download something that you don't trust. Don't download cracked/hacked games/apps. Don't download apps that claim to hack games (like free gold/gems/whatever).
Android apps are "sandboxed", which, simply puts, means true viruses can't do anything (if they even exist). Apps can't mess with other apps, and downloaded apps can't cause changes to "system" apps (the ones you can't uninstall). Now, if you've rooted your device, the rules change, but if you're not rooted...if you don't even know what "rooted" means, then you don't need to worry about this because it doesn't apply to you.
Therefore, any app claiming to be "anti-virus" is BS. Scans slow your device down and drain your battery. Most annoy the crap out of you with notifications. Or give you a sense of security that you should already have in the first place, because of everything I just told you.
A few more things:
Don't bother with task killers, memory managers, RAM boosters, or whatever they might be called. Android doesn't work like Windows. When an app is loaded, it boots from storage, and then remains in memory (RAM) so it can be quickly retrieved. That's why although it takes several seconds to load the first time, it loads nearly instantly afterwards. If too much RAM is being used, Android will kill apps on its own. An app like Clean Master might say that 92% of your RAM is used, "Boost now!". No. Don't do it. 92% of your RAM being used is a good thing. That's what the RAM is there for. If you "boost", "clean", "kill", whatever, you kill all the apps that you've been using, and now when you want to use them again, they have to re-load from storage, taking more time, more processing power, and more battery. And then you're at 92% again. If, say, you've been using a memory hogging app/game and don't plan on using it again for a good while, then by all means, open the app switcher and swipe it away to kill it. But killing all the tasks doesn't speed up your phone; it does the opposite.
"Battery saver" apps are also pure bunk. Just turn off the wi-fi if you're on the go. Don't bother turning it off if you're connected, but not using it, because this doesn't cause battery drain - data being sent/received does, as does searching for connections. The biggest battery killer is the screen. Turn down the brightness if you're worried about battery life. A lot of "battery saver" apps are also task killers. Apps running in the background don't drain the battery, unless they auto-run anyway (like Facebook or a weather app). Don't worry about Angry Birds or Netflix draining the battery if you switch to doing something else. Killing it will only make the battery drain more if you need to load it again (but again, if you don't plan on using it again for a while, go ahead and kill that specific app). Even apps that are always running to receive "push notifications" (Facebook, email, a game telling you your energy is full) take an insignificant amount of battery
when idle, so don't worry about those either.
Apps like 360 Security might be useless when it comes to fighting malware or boosting your device's speed, but most aren't completely useless. Many, like Lookout, have other security features built-in, such as trackers and kill switches if your device gets lost or stolen. But these features can be had from other apps that won't bog down your device with useless scans and obnoxious notifications.
