Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 15 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. The probability that the operator is busy =.50 What is The average time that a caller must wait before reaching the operator = minutes (round your response to two decimal places).
Added by Hannah D.
Step 1
The service rate is the reciprocal of the average service time. In this case, the service time is 15 seconds, or 0.25 minutes. So, the service rate is 1/0.25 = 4 calls per minute. The traffic intensity (Ļ) is then the arrival rate (Ī») divided by the service rate Show moreā¦
Show all steps
Close
Your feedback will help us improve your experience
Nidhi Singhi and 54 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 1.5 per minute. The average time to handle each is 10 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation. a) The probability that the operator is busy = (round your response to two decimal places). b) The average time that a caller must wait before reaching the operator = minutes (round your response to two decimal places). c) The average number of calls waiting to be answered = calls (round your response to two decimal places).
Supreeta N.
Calls arrive at Lynn Ann Fish's hotel switchboard at a rate of 2.0 per minute. The average time to handle each is 10 seconds. There is only one switchboard operator at the current time. The Poisson and negative exponential distributions appear to be relevant in this situation: a) The probability that the operator is busy (round your response to two decimal places) b) The average time that caller must wait before reaching the operator minutes (round your response to two decimal places) c) The average number of calls waiting to be answered calls (round your response to two decimal places)
Madhur L.
Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. (a) What is the mean time until the one-hundredth call? (b) What is the mean time between call numbers 50 and $80 ?$ (c) What is the probability that three or more calls occur within 15 seconds?
Continuous Random Variables and Probability Distributions
Erlang and Gamma Distributions
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD