Cfrgtkky

I am using randn in MATLAB to generate a set of random numbers for a given mean and standard deviation.

b=5000;

a=500;

y = a.*randn(100,1) + b;

sprintf('%fn',y)

I expect that numbers generated would lie between 4500 to 5500. But, I see values in the range of 3000 to 6000.

Could someone explain why this happens?

Or is there any way to specify that the values should lie between mean plus/ minus 1 SD ?

Or is there any way to specify that the values should lie between mean plus/ minus 1 SD ?

No, by definition.

If yo are using the normal distribution (randn) then you can not really limit your numbers to be in a range, as in the normal distribution only infinity and minus infinity have zero probability, the rest, while having a minuscule probability, can happen.

Alternatively, you can use a different distribution, such as uniform (rand) to constrain the randomness to a gap.

The reason why the values do not lie in the interval [4500,5500] is that the numbers coming out of randn() are not confined to the interval [-1,1], which is why your approach does not work as you intend, even though the general approach makes sense. The numbers coming from randn are drawn from the standard normal distribution, which has a standard deviation of one and a mean of zero. Theoretically, any value between -inf and +inf can come out of randn.

You could do one of the following two things, depending on what you want to do after and how that constrains your options:

Option 1 is to generate your random numbers and divide by the maximum absolute value before you do anything else, i.e.:

z = randn(100,1);

z = z / max(abs(z));

y = 5000 + 500*z;

this will make sure that z does not contain any values smaller than -1 or larger than +1 (note that it does guarantee that at least one of these (-1 or +1) will be present in the array z). You can then use your values of b and a to translate the values to random numbers in the interval of your choice.

Edit: note (as pointed out in the comments on this answer) that while the above option will give you random values in the interval of your choice, it will also alter the distribution and standard deviation associated with these values. If it is important for you that the values follow a normal distribution, do not use this option.

Option 2 is to use rand(), which always returns numbers from the interval [0,1]. Note that these come from a uniform distribution, not a normal distribution. You can then first translate these values to the interval [-1,1]:

z = rand(100,1);

z = 2*z - 1;      % Translates the interval from [0,1] to [-1,1]

and then generate your numbers as before; y = 5000 + 500*z;.