The number of hours a battery lasts before failing varies from battery to battery. The distribution of failure times follows an exponential distribution), which is strongly skewed to the right. The distribution of burnout times is strongly skewed to the right. The central limit theorem says that:

a) as we look at more and more batteries, their average failure times gets closer to the mean (mu) for all batteries of this type.
b) the average failure time of a large number of batteries has a distribution of the same shape (strongly skewed) as the distribution for individual batteries.
c) the average failure time of a large number of batteries has a distribution that is close to Normal.