You don't need to estimate the distribution of the ages of the people you have polled unless of course you don't know the ages of the people you have polled. Y

You don't need to estimate the distribution of the ages of the people you have polled unless of course you don't know the ages of the people you have polled. You have two distributions of ages here; both are known (within reasonable comparatively minute errors), no need to estimate. The distribution of ages of the electorate, strictly not known, but so so close to known compared to all the other estimates you have to deal with. And the distribution of the ages of your pollees, you simply ask them their age (estimating whether they are lying to you about their age is an infinitely deep philosophical hole you'll never get out of).