Let's say I play a game with where the outcome can be any even number from 10 to 30, with unknown probabilities. After playing this game, I have the following results:
$\bar X=20, s=3$ (with $n=1000$)
If I were to calculate the 95% confidence interval, using the formula:
$\bar X \pm 1.96\cdot s/\sqrt n$
- Is this even valid given that the underlying distribution is discrete?
- Disregarding #1, am I correct in assuming that the resulting confidence interval tells me that
the true mean will lie inside this range 95% of the time?
- Similarly, am I correct in assuming that it does not tell me that
the outcome value will lie within this interval 95% of the time?
- How can I find the 95% confidence interval for the outcome values?