Probability and lifetime of a lightbulb

[SUchica10]

This probability problem is for my calculus class...

a) A type of lightbulb is labeled as having an average lifetime of 1000 hours. It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean = 1000. Use this model to find the probability that a bulb
(i) fails within the first 200 hours
(ii) burns for more than 800 hours

b) What is the median lifetime of these lightbulbs?

 

[radou]

Show us some work. You must have learned something about probability density functions in your class that is just enough to get started.

 

[SUchica10]

My teacher does not explain well and I don't know where to start... I am thinking that I will need to integrate but I am not sure what the function would be.

 

[Office_Shredder]

It's reasonable to model the probability of failure of these bulbs by an exponential density function with mean = 1000.

What does this tell you off the top of your head? Try graphing what such a function must look like

 

[jacinda10]

Why don't you try standard deviation? Or the standard-normal curve? That is how I would go about solving this...

 

[meee]

u know that the area under the curve must be 1
and the mean must be 1000

now make a friken model.

jacinda10 i don't think this is normally distributed

 

[HallsofIvy]

Why don't you try standard deviation? Or the standard-normal curve? That is how I would go about solving this...

In spite of the fact that the problem says it is an exponential distribution?

SUchica10, as I just said, you are told that the distribution is exponential. Have you looked up "exponential distribution" in your textbook?

 

[Playdo]

The way to handle any question like this , no matter the distribution (well there are some pathological examples but they are rare) is to integrate. So integrate under that probability distribution from 0 to 200 and then 800 to infinity. As long as you have normalized the distribution the result is the probability you seek.