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?