Gaussian Random Process with Unit Mean

I want to generate a Gaussian Random Process with Unit Mean(mean=1) in MATLAB. I tried to do randn function but I later learned that it can be only used when mean is 0 so I tried to write the process by hand. I wanted to write the Gaussian function with mean = 1 and var = 1. I tried this code:

N = rand(1000,1);

g1 = (1/(sqrt(2*pi)))*exp(-((N-1).^2)/2);

plot(g1)

m = mean(g1)

v = var(g1)

However, when I check the mean and variance values I get m=0.3406 and v=0.0024. Can you help?