Solution Found!
The time between calls is exponentially distributed with a
Chapter 4, Problem 204SE(choose chapter or problem)
Problem 204SE
The time between calls is exponentially distributed with a mean time between calls of 10 minutes.
(a) What is the probability that the time until the first call is less than five minutes?
(b) What is the probability that the time until the first call is between 5 and 15 minutes?
(c) Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90.
(d) If there has not been a call in 10 minutes, what is the probability that the time until the next call is less than 5 minutes?
(e) What is the probability that there are no calls in the intervals from 10:00 to 10:05, from 11:30 to 11:35, and from 2:00 to 2:05?
(f) What is the probability that the time until the third call is greater than 30 minutes?
(g) What is the mean time until the fifth call?
Questions & Answers
QUESTION:
Problem 204SE
The time between calls is exponentially distributed with a mean time between calls of 10 minutes.
(a) What is the probability that the time until the first call is less than five minutes?
(b) What is the probability that the time until the first call is between 5 and 15 minutes?
(c) Determine the length of an interval of time such that the probability of at least one call in the interval is 0.90.
(d) If there has not been a call in 10 minutes, what is the probability that the time until the next call is less than 5 minutes?
(e) What is the probability that there are no calls in the intervals from 10:00 to 10:05, from 11:30 to 11:35, and from 2:00 to 2:05?
(f) What is the probability that the time until the third call is greater than 30 minutes?
(g) What is the mean time until the fifth call?
ANSWER:
Solution
Step 1 of 7
Let X be the time between the calls
And X is exponentially distributed with mean of 10 minutes
Then Mean=
Then
The cdf of exponential distribution
a) We have to find the probability of the time until the 1st call is less than 5 minutes
Now find
=1-0.6065
=0.3935
Hence the probability of the time until the 1st call is less than 5 minutes is 0.3935