It can be a "normal" outcome after a night of drinking, however it is not "normal" in terms of health. To avoid unfavorable / unhealthy outcomes from drinking, a person should maintain moderate (safe) drinking limits, which are defined as:

For women: no more than 7 in a week, with no more than 3 of those 7 on any given day.

For men: no more than 14 in a week, with no more than 4 of those 14 in any given day. 

Part of this concept of staying within safe limits is to know that not all drinks are alike. "A" drink is either 5 ounces of wine OR 12 ounces of beer OR 1.5 ounces of spirits (e.g., vodka). Many bar or restaurant drinks contain more than one standard drink, so a person needs to watch not only the number of drinks but the drink size and content, as well.

One further note: binge drinking - which is a problem - is considered 4 or more standard drinks for women and 5 or more standard drinks for men.