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The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 15 people per hour. The inter-arrival time, X, is defined as the time that passes between successive arrivals of patients seeking medical attention. (a) It has been 4 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 9 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors? Use four decimals in your answer.

The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 15 people per hour. The inter-arrival time, X, is defined as the time that passes between successive arrivals of patients seeking medical attention. (a) It has been 4 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 9 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors? Use four decimals in your answer.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 61CR
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The number of people arriving per hour at the emergency room (ER) of a local hospital seeking medical attention can be modeled by the Poisson distribution, with a mean of 15 people per hour.

The inter-arrival time, X, is defined as the time that passes between successive arrivals of patients seeking medical attention.

(a) It has been 4 minutes since the last person seeking medical attention arrived at the ER. What is the probability that at least 9 minutes (in total) will pass until the next medical-attention-seeking person passes through the ER doors? Use four decimals in your answer.

A certain section of a Northern Alberta forest is undergoing a pine-beetle infestation. A biologist has determined that the number of pine-beetle infected trees fluctuates from acre to acre, with an average of 10.6 pine-beetle infected trees per acre. (c) As a way to combat the infestation, the infected trees are to be sprayed with an insecticide at a cost of $3 for every tree infested with pine beetle(s), plus an overhead fixed cost of $60 for equipment rental. Letting Cost represent the total cost for spraying all the pine-beetle infested trees for a randomly chosen acre of forest. Find the expected cost of spraying an acre. In addition, find the standard deviation in the cost of spraying an acre. E(Cost) = $ 81.8 (use two decimals) SD(Cost) = $ 9.7673 (use two decimals)
Transcribed Image Text:A certain section of a Northern Alberta forest is undergoing a pine-beetle infestation. A biologist has determined that the number of pine-beetle infected trees fluctuates from acre to acre, with an average of 10.6 pine-beetle infected trees per acre. (c) As a way to combat the infestation, the infected trees are to be sprayed with an insecticide at a cost of $3 for every tree infested with pine beetle(s), plus an overhead fixed cost of $60 for equipment rental. Letting Cost represent the total cost for spraying all the pine-beetle infested trees for a randomly chosen acre of forest. Find the expected cost of spraying an acre. In addition, find the standard deviation in the cost of spraying an acre. E(Cost) = $ 81.8 (use two decimals) SD(Cost) = $ 9.7673 (use two decimals)
The number of people entering a security check-in lineup in a 15-minute interval at a medium sized airport can be modeled by the following probability model: P(X = x) = e 1"(17)- x = 0, 1, 2, ... Part (d) In the past 15-minutes, you have been told that somewhere between 13 and 19 people, inclusive, have entered the security lineup. Compute the probability that this uncertain number is 17. (use four decimals in your answer)
Transcribed Image Text:The number of people entering a security check-in lineup in a 15-minute interval at a medium sized airport can be modeled by the following probability model: P(X = x) = e 1"(17)- x = 0, 1, 2, ... Part (d) In the past 15-minutes, you have been told that somewhere between 13 and 19 people, inclusive, have entered the security lineup. Compute the probability that this uncertain number is 17. (use four decimals in your answer)
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