# Thread: help me with this problem

1. ## help me with this problem

• The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes.
(i) What is the probability that there are no calls within a 30 minute interval?
(ii) What is the probability that at least one call arrives within a 10 minute interval?
(iii) What is the probability that the first call arrives within 5 and 10 minutes after opening?
(iv) Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90.

Thanks!

2. Originally Posted by arundathi
• The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of 15 minutes.
(i) What is the probability that there are no calls within a 30 minute interval?
(ii) What is the probability that at least one call arrives within a 10 minute interval?
(iii) What is the probability that the first call arrives within 5 and 10 minutes after opening?
(iv) Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90.

Thanks!
This is also Poisson with mean of 2 calls/30 minutes, so for (i)...

$F(0) = \frac{e^{-2}(2^0)}{2!}$
$= .0677$

I'll leave the rest up to you for now.