Yes. This is entirely normal and to be expected since you two didn't have a father-daughter relationship when you were growing up, and an emotional bond wasn't formed. You led separate lives, and he didn't take on the responsibility of being a dad: tucking you into bed at night, attending your dance recitals and ball games, helping you with homework, and making you feel like a loved and cherished child. You don't have shared memories of good times and bad so, yes, you two are strangers to one another.
You can still build a strong relationship now if both of you are willing to put in the time and effort. You, however, are now facing adulthood and have many new and interesting possibilities in front of you. At this point in your life, you may not have a strong desire to reconnect with your dad because friends, college, career, travel, and romantic possibilities are all in front of you. You may not want to reach back in the past but rather look forward.
The choice is entirely yours. You have no obligation towards your father. It was he who had obligations to you that were left unfulfilled. You have no responsibility to make him feel better and less guilty about the mistakes he made. He must deal with those on his own.
You may be having a hard time conversing with him because you're avoiding the tough questions. It's best to be straightforward and honest with him about what you're thinking and feeling. Have you asked him to explain why he didn't get in contact with you all those years? Did he pay child support, and if not, why not? What was he doing during that time? What does he want from the relationship now? Why should you trust him now when he dropped out of your life? If you can't have big conversations like these, you won't get closer.
You may want to see a counselor for a short period to work through your relationship with your dad. You don't want to take the issues you've had with him into future relationships with men. I also have another article that hopefully will be helpful called “5 Steps to Heal Her Pain: How a Fatherless Daughter Can Move on From a Dad's Rejection.”