e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hour

Question

Nitella [24]

2 years ago

8

e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hour

s. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean

Mathematics

1 answer:

Tcecarenko [31] · Answer 1 · 2022-07-19T07:32:51+03:00

Tcecarenko [31]2 years ago

8 0

Answer:

Step-by-step explanation:

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