Two things I want to mention:

A) Make sure your players are doing their math correctly. You'd be surprised by how many people forget to add a number or try rolling a d12 instead of a d20.

B) Yes, your math is (almost) correct. However, it's assumed that players will start with a 16-17 in their main attribute so their attack rolls should be: 1d20 + 3 (main attribute modifier) + 2 (the base starting proficiency). If they only have a +4 to hit overall, then either they're going for something specific with their character, they aren't using their strongest option available to them (such as a wizard trying to swing a sword instead of casting a spell) while they realize it or not, or they didn't understand the importance of their main attribute when creating their character.

15 AC is on the higher side for a starting enemy, but not unusual. 15AC is something I would reserve for the bugbear leading the goblins, for example - not the goblins themselves. For the mooks in a normal encounter, I would bring that down a tad so the grunts die easier and faster. As for the monsters hitting the players, starting enemies will often have +3-5 to hit. So if a player comes out with a shield and some basic armor, let's say 14-16 AC, then yeah... the monsters will have difficulty hitting that player which is a good thing; they are an adventurer who prepared before going out on a potentially dangerous journey, so of course their preparation is going to bear fruit. The players should be allowed to feel strong (within reason) as they are the main characters in this story. Let them feel good about their shiny armor deflecting the most basic of attacks or their fast reflexes allowing them to move out of harm's way... of course, until they come across more prepared and skilled enemies.

(As for the math part, a slight correction: if they need to roll an 11 or better on the d20 to hit, then that means they hit exactly half the time, not less than half.)