A call centre can be modelled by a Poisson process with a rate of 1 call per minute.
1. What is the probability of no calls between 9 am and 9:05 am on a given morning?
2. Given that there have been no calls on a particular morning between 9 am and 9:05 am, what is the probability of exactly one call between 9:05 am and 9:10 am?
(Please attach a detailed explaination, thx)
Explanation:
Given 1 call per minute.
Poisson distribution formula is
1. probability of no calls between 9 am and 9:05 am on a given morning
9am to 9:05 am : 5 minutes.
So λ is 5.
No calls means x=0.
2.Given that there have been no calls on a particular morning between 9 am and 9:05 am, the probability of exactly one call between 9:05 am and 9:10 am. This can be calculated by using conditional probability.
P(a/b) = p(a and b)/p(b)
Let p(a) as 9:05 to 9:10 one call
Let p(b) as 9 to 9:05 no calls.
9:05 to 9:10 5 mins .
So lamdba is 5.
And having exactly one call so x=1.
This is p(a).
P(a/b) = p(a) since independent events.
The number of calls during 9 to 9:05 will not effect the calls during 9:05 to 9:10
A call centre can be modelled by a Poisson process with a rate of 1 call...
n a call centre, the number of calls an attendant answers follows a Poisson istribution with a mean of 5 calls per hour. The company has 8 attendants. a) What is the probability that an attendant answers only one call in one hour? b) What is the probability that two (out of the eight) attendants answer only one call in one hour?
A company has a customer services call centre. The company believes that the time taken to complete a call to the call centre may be modelled by a normal distribution with mean 16 minutes and standard deviation σ minutes. Given that 10% of the calls take longer than 22 minutes, (a) show that, to 3 significant figures, the value of σ is 4.68.(3) (b) Calculate the percentage of calls that take less than 13 minutes.(1) A supervisor in the call centre claims that the mean...
Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such that, λ(t)-0.5 calls/hr for 0<ts? hr, λ (t)-0.9 calls/hr for 7<ts17 hr, and λ(t)-1.3 calls/hr for 17<ts24. a. Find the probability that there are no calls between 6 am and 8 am. b. Find the probability that there are at most 2 calls before noon. c. What is the probability that there is exactly one call between 4:50 pm and 5:10 pm? d. What is...
3. Telephone calls are received at an emergency 911 number as a non-homogeneous Poisson process such that, λ (t)-0.5 calls/hr for 0<ts7 hr, λ(t)-09 calls/hr for 7<ts17 hr, and λ (t)-1.3 calls/hr for 17<ts24 a. b. c. d. Find the probability that there are no calls between 6 am and 8 am. Find the probability that there are at most 2 calls before noon What is the probability that there is exactly one call between 4:50 pm and 5:10 pm?...
Assume that you run a call center that receives an average of 3 calls per minute with a Poisson distribution. Use this information to answer questions 1 to 4. What is the probability that the call center receives exactly 2 calls in the next minute? Use the formula and show your work. What is the probability that the call center receives exactly 4 calls in the next minute? What is the probability that the call center receives exactly one call...
1. The main office of a business receives phone calls according to a Poisson process, at an average rate of 3 calls per 10 minutes. What is the probability that over a 30 minute interval there will be at least 10 calls received ?
The number of requests for assistance received by a towing service is a Poisson process with rate θ = 4 per hour. a. Compute the probability that exactly ten requests are received during a particular 2-hour period. b. If the operators of the towing service take a 30-min break for lunch, what is the probability that they do not miss any calls for assistance? c. How many calls would you expect during their break?
1) The number of calls received at a certain information desk has a Poisson Distribution with an average of 6 calls per hour. (15 points) (a) Find the probability that there is at exactly one call during a 15 minute period. (You cannot use tables here - show all work) (b) Find the probability that at least 6 calls are received during a 30 minute period. (you may use tables here) ******************************** 2) Note that for the above problem, the...
Particles are emitted by material with wet radioactivity according to Poisson process with a rate of 10 particles emitted every half minute, which is to say the time between two emissions is independent of each other and has an exponential distribution. 1) What is the probability that (after ) the 9th particle is emitted at least 5 seconds earlier than the 10th one ? 2) What is the probability that, up to minutes, at least 50 particles are emitted? Write...
Problem 2. Customers arrive at a call center according to a Poisson process with rate 6/. (a) Find the probability that the 5th call comes within 10 minutes of the 4th call. (b) Find the probability that the 9th call comes within 15 minutes of the 7th call.