mean = 0
variance = 1
samples = 100000

# vectors
a = np.random.normal(mean, variance, samples)
b = np.random.normal(mean, variance, samples)
c = np.random.normal(mean, variance, samples)

# weights
weight_a = 0.3
weight_b = 0.3
weight_c = 0.4

result = (a * weight_a) + (b * weight_b) + (c * weight_c)
print(np.mean(result), np.var(result))
# 0.001295722463321136 0.34123206614565454