Member of multiple normally distributed populations I'm writing a little tool for work and a stats question has arisen that is beyond me. In layman's terms:
Let's say I've got a sample of 50 people who read the WSJ and their ages are normally distributed with a mean of 45 and a standard deviation of 10.
I've got a sample of 100 people who read the NYT. Mean age: 40, std. dev. 8.
And I've got a sample of 36 people who read E Weekly. Mean age: 30, std dev: 15.
Then this new user comes in, and I don't know his age, but I know he reads WSJ AND NYT AND E WEEKLY. How do I quickly find the age that is most likely? Do the sample sizes matter?
Thanks!
 A: You are specifying sample estimates of age conditional on being a reader of each magazine (with no other information specified)
So we know estimates of
$E(Y|M_1)$, $E(Y|M_2)$, $E(Y|M_3)$  (and of their variances). 
But now you seek $E(Y|M_1,M_2,M_3)$ (and its variance). 
The problem is that we don't know how they interact. Within the NYT readers, the sub-population of those who read E.Weekly may differ from the population overall in a way that doesn't relate simply to the means for the two magazines.
It may be that people who read both are on average much younger than a typical NYT reader of unknown status. Or much older. Or about the same.
So your question doesn't specify enough information to answer. Without additional information or additional assumptions, your question cannot be answered.
--
If we were to assume independence, what could be done?
In that circumstance, we could add the effects of reading each magazine. But to estimate those effects, we either need to know additional information, such the overall population mean age, where 'population' is the same population as that surveyed (e.g. 'people who might read magazines or papers'); not the wider population of the country - five-year-olds don't read those publications. Alternatively we'd need information such as the average age of those who don't read each magazine or newspaper (again, with the same definition of population) and perhaps the proportions (I haven't worked this case through). We'd also need to make some assumptions about our sampling.
So for example, the "age-effect" of reading the NYT would be:
$$E(Y|M_1)-E(Y)$$
and similarly for the other two magazines/papers. Then
\begin{eqnarray}
E(Y|M_1,M_2,M_2) &=& E(Y) + \\
& &\,\,[E(Y|M_1)-E(Y)] + [E(Y|M_2)-E(Y)] + [E(Y|M_3)-E(Y)]
\end{eqnarray}
would be the population quantity we're trying to estimate. If you have a random sample of the target population, you should be able estimate these by replacing them with their sample estimates.

can I just maximize $p(\text{age} | \text{WSJ}, \text{NYT}, \text{EW})$ using Bayes rule and the independence assumptions to flip everything around and employ normal pdfs

Good question.
$P(\text{age} | \text{WSJ & NYT & EW})=P(\text{age}, \text{WSJ & NYT & EW})/P( \text{WSJ & NYT & EW})$
$=P( \text{WSJ & NYT & EW}|\text{age})P(\text{age})/P( \text{WSJ & NYT & EW})$
now apply independence
$=[P( \text{WSJ}|\text{age})P( \text{NYT}|\text{age})P( \text{EW}|\text{age})]P(\text{age})/P( \text{WSJ & NYT & EW})$
So you need:
$P( \text{WSJ}|\text{age})$
$P( \text{NYT}|\text{age})$
$P( \text{EW}|\text{age})$ 
$P(\text{age})$
$P( \text{WSJ & NYT & EW})$
(You can apply independence again to reduce that last one to a product)
If you can find or work out values for all those, you're done.
