Calls to the help line of a large computer distributor...

Name: Problem 144, Chapter 4: Applied Statistics and Probability for Engineers
Uploaded: 2021-12-29T02:59:30-08:00
Duration: 2 min 24 s
Channel: Amany Waheeb
Description: Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. Determine the following: (a) Mean time until the one-hundredth call (b) Mean time between call numbers 50 and 80 (c) Probability that three or more calls occur within 15 seconds

Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. Determine the following: (a) Mean time until the one-hundredth call (b) Mean time between call numbers 50 and 80 (c) Probability that three or more calls occur within 15 seconds

Calls to the help line of a large computer distributor follow a Poisson distribution with a mean of 20 calls per minute. Determine the following:
(a) Mean time until the one-hundredth call
(b) Mean time between call numbers 50 and 80
(c) Probability that three or more calls occur within 15 seconds

Key Concepts

Poisson Process

A Poisson process is a statistical model that describes events occurring randomly over time, where the events happen independently and at a constant average rate. This process is widely used in fields such as telecommunications, queuing theory, and reliability engineering to model random events like customer arrivals or calls to a help line.

Exponential Distribution

The exponential distribution describes the waiting times between successive events in a Poisson process. It has the memoryless property, meaning that the probability of an event occurring in the future is independent of how much time has already elapsed. This distribution is commonly used to model the time between arrivals or failures.

Gamma Distribution

The gamma distribution generalizes the exponential distribution and is used to model the waiting time until the nth event in a Poisson process. Essentially, the time until the kth event can be seen as the sum of k independent exponential waiting times, making the gamma distribution a key tool when dealing with cumulative event times.

Poisson Distribution

The Poisson distribution models the number of events that occur in a fixed interval of time or space when these events happen independently and with a known constant rate. It is particularly useful for calculating probabilities of a specific number of events occurring in a given timeframe, such as the probability of receiving a certain number of calls within a specified interval.

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