randn command variance problem

Hello, i am trying to create a randomly distributed temperature where the avarage is 310 and variance is 4.

I wrote the following code, but as could be seen from the plot bellow it gives me values of 318 ,301 which are far away from variance 4.

Where did i go wrong?

Thanks

n=100000;
Temp_rand=2*randn(n,1);
T = 37+273+Temp_rand;
plot(T);
xlabel('sample number');
ylabel('Temperature');

Answer 1

[Ameer Hamza]

In a normal distribution, the variance is not the maximum limit between two random numbers. A single random number can go way beyond the variance (but the probability of that happening is extremely small). If you want to have a strict limit, then use uniform random numbers. For example,

n=100000;
min_value = 27+273-4;
max_value = 27+273+4;
T = min_value + (max_value - min_value) * rand(n,1);
plot(T);
xlabel('sample number');
ylabel('Temperature');
ylim([min_value-2, max_value+2]);

[Steven Lord]

To supplement what Ameer Hamza said, for your original data set let's look at the bounds and the statistical properties of the data set.

n=100000;
Temp_rand=2*randn(n,1);
T = 37+273+Temp_rand;

M = mean(T);
V = var(T);
[N, X] = bounds(T);

[N, M, X, V]

I've run this several times. The smallest lower bound I've seen is 300.5861 and the highest upper bound is 318.8690. The mean is very close to 310 and the variance is around 4 in all my trials.