I have a problem where in a group of users, 55 of them get 203 emails/month with a std.dev = 5 and 85 of them get 205 emails/month with std.dev = 6.
What information can be derived from this information. Example What can we tell about two sub populations and their differences?
What type of information we can say about confidence intervals.
What calculation I can carry out?
Trying to learn basic via problem solving.
You have to define what questions you are trying to ask. In statistics, people tend to assume a normal distribution. If that is correct, because the difference of the means is small compared to the standard deviations, from one sample you cannot tell which population it comes from. If you had a bunch of people that you knew came from the same group, you could ask how many you would have to sample to have some confidence that you knew which group they came from.
On the other hand, maybe the first group all got $202$ or $203$ e-mails except for a couple people who got so many the average was $203$ and the standard deviation was $5$ and similarly the second group all got $204$ or $205$ except a couple to make the standard deviation high. You could tell from one person which group they came from if you knew the distribution. Similarly, maybe half the people in the first group got $197$ and half got $208$, while half the people in the second got $199$ and half got $211$. Again you could tell which group an individual came from.