\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The lifespan of a specific battery has mean \(\mu=800\) hours and standard deviation \(\sigma=60\) hours. A technician tests a sample of \(n=100\) batteries and calculates the mean lifespan \(\overline{X}_{100}\).
  1. Calculate the expected mean lifespan of the sample.
    \(E(\overline{X}_{100})=\)
  2. Calculate the standard deviation of the sample mean.
    \(\sigma(\overline{X}_{100})=\)