This question is often asked during interviews, e.g. what would the distribution of time spent per day using YouTube or Facebook look like?
If the data do not contain imperfections (e.g., people being AFK on the site or people opening and quickly closing the site), I would expect the distribution to be normal. Is that wrong?
Best Answer
For youtube I think the distribution depends on the distribution of video length. Most videos are about 8 to 10 minutes (this is the average span of the people attention). One might watch 0, 1, 2, or any other number of videos. A Poison distribution might be a good candidate to model the number of visits to a website or the number of videos watched per day. If the distribution of the time of a single video would be $P_V(t)$ then the distribution of total time would be something like $$P_{Total}(t)=\sum_{i}^{} P_p(N=i)P_{Vi}(t)$$ where $i$ is the number of visits, $P_p(N=i)$ is the Poisson distribution and $P_{Vi}$ is distribution of total time of $i$ videos which can be obtained by performing convolution on $P_v$. If $P_v(t)$ is approximately Gaussian then the distribution would be a mixture of Gaussians. Something that looks like the following picture. (I only guessed the distribution, not to scale)
For facebook there might be something similar to a video length. For example the time required to look at one page.