Im trying to generate a list of random (standard) independent normal variables. For this, I first generate a random list of, say, 100 real numbers in the range [0, 1000], and then make them standard independent random variables. However, this strategy is not working in Mathematica. Is there an alternate way to approach this problem?
I think you got what you needed from the comments, but I'll go ahead and post this as further illumination.
Firstly, it's important to note that there's no such thing as a "standard normal distribution" with a "range" (that's how I interpret the OP: you want a range of variates that exhibit a normal distribution): the normal distribution is of infinite extent. Every normal distribution has every real as a possible value.
So, there's a few ways to handle your query, depending on the desired outcome.
Method 1: Taking your desired minimum and maximum, decide how "rare" those extremes need to be, and generate variates with the appropriate mean and deviation. Here's a quick-n-dirty function to do just that. It takes the minimum, maximum, allowed deviation, and a truncation option:
Called like so:
Decreasing the deviation argument means values below or above your specified range become more likely, increasing it makes them less likely. But - because this is a distribution with infinite extent, given enough variates, you might see values outside of your range.
The same function called like so
Another way of range-limiting the results is to use
will generate 20 variates with a mean of 500, deviation of 200, limited to between 400 and 600.
Lastly, one might use
Which will generate 20 variates with a mean of 500, deviation of 200, limited to between 400 and 600 as with
Lastly, a gentle reminder: None of the last three methods are "normal distributions", per se - they are "normal like"...