Question

The lightbulbs used to provide exterior lighting for a large office building have an average lifetime of 700 hours. Suppose that the distribution of the variable

ℎ=length of bulb lifeh can be modeled as a normal distribution with a standard deviation σ=50. How often should all the bulbs be replaced?

a. Every 350 hours
b. Every 500 hours
c. Every 650 hours
d. Every 800 hours

Answer 1

The lightbulbs should be replaced every 650 hours.

Step-by-step explanation:

In this question, we are given that the average lifetime of the lightbulbs used for exterior lighting is 700 hours and the standard deviation is 50. We are asked to determine how often the bulbs should be replaced. To solve this, we need to consider the normal distribution and find the time at which the probability of a bulb lasting beyond that time is very low.

We can answer this question by finding the z-score that corresponds to the desired probability. In this case, we are looking for the time at which the probability of a bulb lasting beyond that time is less than 2% (since we want to replace the bulbs that have the lowest 2% of lifetimes).

We can use a standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 0.02. Using the z-score, we can find the corresponding time value using the formula: time = mean + (z-score * standard deviation).

Plugging in the values from the question, we find that the time at which the bulbs should be replaced is every 650 hours.