Getting a set of random number between 2 numbers that have a certain mean.

Problem: Getting a set of random numbers between two values that will have a certain mean value.

Let say we getting n number of random number where the number will be between 1 and 100. We have a mean of 25.

My first approach is to have 2 modes where we have aboveMean and belowMean where the first random number is the initial range 1 and 100. Every subsequent number will check the total sum. If the total sum is above the mean, we go to case aboveMean which is then get a random number between 1 and 25. If the total sum is below the mean, we do case belowMean then get a random number between 26 and 100.

I need some idea on how to approach this problem beside the crude get a random number to add it to the total then get the average. If it above the mean in question, we get a random number below the mean and so forth. While it does work, doesn't seem to be the best method.

I'm guessing I should brush up on probability to approach this random number generator.