Question

The life expectanct of a typical lightbulb is normally distributed with a mean of 4,000 hours and a standard deviation of 42 hours. What is the probability that a lightbulb will last between 3,875 and 4,055 hours?

Answer 1

use normal distribution to find z

Answer 2

do it involve conditoinal probability

Answer 3

nope

Answer 4

hmm lemme see

Answer 5

There actually is a special formula for exactly this type of tasks.
\[P(\alpha < x < \beta) = \Phi(\frac{\beta - a}{\sigma}) - \Phi(\frac{\alpha- a}{\sigma})\]
where alpha and beta are your bounds. a is mathematical expectation and sigma is square root of variance.

Answer 6

sigma is standart deviation. a is your mean. Phi is a function usualle taken from the table.