How to Generate Normal Random Samples within Mean±3Sigma

I want to draw normal random numbers in an array of order ((100*8)*5000) with a specific Mean (M) and Standard Deviation (S) but I want them to be only within the range M±3S, so that I don't have any outliers in my array exceeding those limits.

Any Suggestion? I want to write a program in R based on this array for some simulation studies.