In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume the messages arrive at the node according to a Poisson process with (lambda = 32) messages per minute. Five messages are used to form a packet. Round your answers to three decimal places (e.g. 98.765). a) What is the mean time until a packet is formed, that is, until five messages arrived at the node? 9.375 seconds b) What is the standard deviation of the time until a packet is formed? 9.375 seconds c) What is the probability that a packet is formed in less than 10 seconds? 0.656 d) What is the probability that a packet is formed in less than 5 seconds? 0.413
Added by Marta G.
Close
Step 1
375 seconds. Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 86 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
In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume the messages arrive at the node according to a Poisson process with λ = 26 messages per minute. Five messages are used to form a packet. Round your answers to three decimal places (e.g. 98.765). a) What is the mean time until a packet is formed, that is, until five messages arrive at the node? b) What is the standard deviation of the time until a packet is formed? c) What is the probability that a packet is formed in less than 10 seconds? d) What is the probability that a packet is formed in less than 5 seconds?
Supreeta N.
In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume the messages arrive at the node according to a Poisson process with $\tau=30$ messages per minute. Five messages are used to form a packet. (a) What is the mean time until a packet is formed, that is, until five messages have arrived at the node? (b) What is the standard deviation of the time until a packet is formed? (c) What is the probability that a packet is formed in less than 10 seconds? (d) What is the probability that a packet is formed in less than 5 seconds?
Continuous Random Variables and Probability Distributions
Erlang and Gamma Distributions
4-116. In a data communication system, several messages that arrive at a node are bundled into a packet before they are transmitted over the network. Assume that the messages arrive at the node according to a Poisson process with λ = 25 messages per minute. Five messages are used to form a packet. (a) What is the mean time until a packet is formed, that is, until five messages have arrived at the node? (b) What is the standard deviation of the time until a packet is formed? (c) What is the probability that a packet is formed in less than 12 seconds? (d) What is the probability that a packet is formed in less than 6 seconds?
Adi S.
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
