The time (sec) that it takes a librarian to locate an entry in a file of records on checked-out books has an exponential distribution with lambda symbol=0.5.

Question

a)What proportion of all location times are less than 20 sec? At most 20 sec? Atleast 25 sec/ Between 10 sec and 25 sec?

I know the function is f(x)=0.5e^(-0.5x). If I take the integral of the function from 0 to 20, will that give me the answer. Because I got 1, so can you please check if 1 is the right answer for P(x<20).

Then less than 20 is: p(x<20)
betwen 10 and 25 is P(10<x<25)
how do I write at most 20 and at least 25?

Answer 1

You wrote:
How do I write at most 20 and at least 25?

At most 20:
P(x ≤ 20)
At least 25:
P(x ≥ 25)

Someone else may be able to help you with the function.