The lifetime of certain electronic components is a random variable with the expectation of 5000 hours and a standard deviation of 100 hours. What is the probability that the average lifetime of 400 components is less than 5012 hours?
When I calculated this answer I was not sure how to include 400 items into what I know about standard deviation but assuming the probability works much like calculating consecutive coin flips (Ex: 1 heads = 1/2^1, 2 heads = 1/2^2, n heads = 1/2^n) I just used the standard deviation of .12 and then added 400 as the exponent to get a ridiculously small number which makes me feel very unconfident.
My assumption:
P(400 items <= 5012 hours) = I(.12)^400 = .5478^400 = 2.810678e-105