If I have a box with 2 types of light bulbs, A and B. The lifespan of each type of lightbulb follows a gaussian distribution A ~ N(1000h, 5h), and B ~ N(990h, 4h). I know that 70% of them are A and the other 30% are B. How can I know the normal distribution of my box? I think it's obvious that the new mean will beμA*0,7+μB*0,3, but how can I know the new standard deviation? Or maybe I just can't?