Is it normal for someone to have anemia?

No. It is not normal to be anemic. Your body has ability to maintain a good status all the time. If you are anemic it means that those mechanisms have been overwhelmed and cannot keep anymore a proper balance. You should see your pcp and after some iron therapy if still anemic a more in depth work-up will be needed.
Not normal..Anemia. Is an hematocrit outside the normative values for age and sex. Its presence can be detected by a complete blood count (cbc). The hematocrit is the volumetric percentage of our peripheral blood occupied by red blood cells. Typically, hematocrit (hct) for a woman is lower than for a man of the same age. Why the anemia is present is another matter, and requires investigation then correction.