Question

e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean

Answer 1

Explanation:

`p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\frac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \frac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}`