1) I generate 1000 random numbers between 0 and 10 and take the average.
If I do the above action "many" times the resulting average values will be a normal distribution over 0 to 10. Correct?
What I want after "many" iterations of generating 1000 random numbers (+ some manipulation) is to produce average values between 3 and 7, distributed evenly between 3 and 7.
What's my approach here?
Best Answer
You could generate $1000$ randoms, average them to find the mean $\mu_0$, generate one more random evenly distributed between $3$ and $7$ for $\mu$, the mean you want and add or subtract $\mu-\mu_0$ from all the original $1000$. This will likely shift some of the randoms out of the original interval. Does this meet your needs?