B Natural exponential function, calculus

[Medtner]

So I'm trying out various practice problems and for some reason I can't get the same answer when it comes to problems involving natural exponentials.

Here's the problem
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 μ = 1000.

a)
Use this model to find the probability that a bulb fails within the first 200 hours.

Did the work, all fine and dandy, integration and what not and it led me to this:

-e^1/5 + 1
Book says the answer is 0.81
However when I evaluate it on my calculator its -.0221402

Don't know what I'm doing wrong, please help.

 

[ramzerimar]

I'm pretty sure the answer would be 0.81 if we are talking about the bulb failing after 200 hours: P(X>200).

Also, make sure you have your signals right. You can't have negative probabilities, as you probably know.

 

[mathman]

So I'm trying out various practice problems and for some reason I can't get the same answer when it comes to problems involving natural exponentials.

Here's the problem
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 μ = 1000.

a)
Use this model to find the probability that a bulb fails within the first 200 hours.

Did the work, all fine and dandy, integration and what not and it led me to this:

-e^1/5 + 1
Book says the answer is 0.81
However when I evaluate it on my calculator its -.0221402

Don't know what I'm doing wrong, please help.

In order to get help for a calculation problem, it is useful to show each step in the calculation.