1. ## Probability

The average life of a light bulb is 500 hours. Find

a)the probability that a bulb will last more than 1,000 hours
b)the probability that a bulb will last less than 100 hours
c)the median life
d)the probability that a bulb will last exactly 500 hours
e)the 95 Percentile

2. Distribution, work you did that was wrong. . .etc.

3. Originally Posted by lisa1984wilson

The average life of a light bulb is 500 hours. Find

a)the probability that a bulb will last more than 1,000 hours
b)the probability that a bulb will last less than 100 hours
c)the median life
d)the probability that a bulb will last exactly 500 hours
e)the 95 Percentile

Is it known what the distribution is that the life of a bulb follows? is the variance or standard deviation known? Without knowing the whole question it's impossible to provide help.

4. That is the full question, and this was is below it.

(Note: From the table on page 722 of your textbook, e^ ( -3.0) is almost 0.05, so the 95 percentile life would be -3.0/0.002 = 1,500 hours)

5. If it's an exponential distribution with an AVERAGE (mu) lifetime of 500 hours, then from your notes you should remember that:

$\displaystyle \mu_x=\frac{1}{\lambda}$

Solving for lambda will allow you to get your parameter lambda.

To find a through e you have to remember that $\displaystyle P(X\leq x)$ is represented by $\displaystyle 1-e^{x\lambda}$, and for $\displaystyle P(X> x)$ is represented by $\displaystyle 1-P(X\leq x)$.

Try to work with that and see where you get, or at least show us the work you did that was determined to be wrong. To help you get started:

A. $\displaystyle P(X>1000)=1-P(X\leq 1000)$. Why? Because to find the probability that a component lasts longer than 1000 hours, we only need to find the compliment of it lasting SHORTER than 1000 hours. So:
$\displaystyle P(X>1000)=1-[1-e^{1000*-0.002}]$

6. thanks I figured it out!