Calculating Probability for Exponential Distribution in Unplanned Shutdowns

[Changoo]

I am having a lot of trouble with a homework question from my book. It asks:

The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 20 days. Find the probability that the time between two unplanned shutdowns is more than 21 days.

I know this much so far 1-e-(20)(?) (one minus e to the negative power of mean times any value of the continuous variable(X))

I am lost on finding X within the equation.

Hope someone can help.

 

[courtrigrad]

Hello!

First of all what do we define as an exponential distribution? It is equaled to:

1 - e^(-yx)

= 1 - e^(-20)(21)

Since this is the probability that the time between two unplanned shutdowns is less than 21 we don't need the 1. Hence our answer (I think) would be:

e^(-20)(21) or essentially 0.

Hope this helps!

 

[Changoo]

Thanks for your help,

But how do I solve E^-(20)(21)? I know that 20 times 21 is 420. How do I determine e^-420?

The book has given me some answers, but none say zero. a. .350, b. .650, c. .150, d. .850

I can probabily figure out the answer with no problem if someone can help me witht the problem above.
Thanks for your help!

 

[Changoo]

Okay, here is what I have, please tell me if I am right:

F(x)=1-e^-(20)(2/21)

F(x)=1-.850

F(x)=.150 (final answer)

I hope I am write.

 

[Changoo]

I meant right**** Sorry

 

[Changoo]

Asking for Review

I feel confident about my answer, I am hoping someone can review and let me know if I have calculated wrong in any way.