(a) What is the shortest time that an insect can be on a plant and stay as long as at least 50% of all insects on the plant? (b) A student is assigned to watch an insect until it flies. They want to know the time that will be exceeded only with a probability of 0.05. (c) If an insect has been observed for 2 minutes without its moving from the plant, what is the probability that it will be there for at least 2 more minutes?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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2 In a particular model of insect behaviour, the time that an insect spends on a plant is
exponentially distributed with a mean of 2 minutes.
(a) What is the shortest time that an insect can be on a plant and stay as long as at least
50% of all insects on the plant?
(b) A student is assigned to watch an insect until it flies. They want to know the time that
will be exceeded only with a probability of 0.05.
(c) If an insect has been observed for 2 minutes without its moving from the plant, what is
the probability that it will be there for at least 2 more minutes?
Transcribed Image Text:2 In a particular model of insect behaviour, the time that an insect spends on a plant is exponentially distributed with a mean of 2 minutes. (a) What is the shortest time that an insect can be on a plant and stay as long as at least 50% of all insects on the plant? (b) A student is assigned to watch an insect until it flies. They want to know the time that will be exceeded only with a probability of 0.05. (c) If an insect has been observed for 2 minutes without its moving from the plant, what is the probability that it will be there for at least 2 more minutes?
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