The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.
Find the probability that the person retired after age 68.

Question

The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 6 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.
Find the probability that the person retired after age 68.

anonymous · Answer

Jesus. I once knew how to do that kind of stuff. 
Tell me the name of that thing your studying so i can remember the formula.

Is it poisson distribution, ANOVA, Variance, ... ?

anonymous · Answer

Um, Exponential Distribution? At least, that's what chapter it was in.

anonymous · Answer

Oh, this is also continuous random variables instead of discrete random variables.

anonymous · Answer

Ok so now i have a problem...

I dont know if i only use values from 60+ or if i have to use the real number as the text says:
We are interested in the time after age 60 to retirement.


The 2 option:

as the mean = 6 and $$mean = 1 / \lambda $$
then  $$\lambda$$= 1/6

P(X) = $$\lambda*e ^{-\lambda*X}$$


P(8) = (1/6)*e^(-(1/6)*8) = 4.4%


OR

mean = 66
P(68) = 0.54%


But i think the correct answer is the first one, 4.4%