Question

Light bulbs used for the exterior walkways of a college campus have an average lifetime of 500 hours. Assume that the lifetime of bulbs is normally distributed with standard deviation 50 hours. Suppose all of the bulbs were replaced at the same time and they have been turned on for a total of 550 hours. What is the probability that a randomly chosen light bulb lasts less than 550 hours?

Answer 1

84.13%

Explanation:

Population mean (μ) = 500 hours

Standard deviation (σ) = 50 hours

Assuming a normal distribution, for any given number of hours 'X', the z-score is determined by:

`z=(X-\mu)/(\sigma)`

For X=550

`z=(550-500)/(50)\\z=1`

For a z-score of 1, 'X' corresponds to the 84.13-th percentile of a normal distribution.

Therefore, the probability of that a randomly chosen light bulb lasts less than 550 hours, P(X<550), is 84.13%.