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Great Geysers! The time (in minutes) between geyser eruptions can be modeled with exponential distribution with mean 90 minutes (1.5 hours). (a) Calculate the probability that it takes between 50 minutes and 100 minutes until the n eruption. (b) Calculate the 95th percentile of times between geyser eruptions. (c) Calculate the probability that the geyser will erupt at least once in the next 2 hours ( minutes). (d) How many times do you expect the geyser to erupt in the next 8 hours (480 minutes)? (e) Calculate the probability that the geyser will erupt exactly 4 times in the next 8 hours.

Great Geysers! The time (in minutes) between geyser eruptions can be modeled with exponential distribution with mean 90 minutes (1.5 hours). (a) Calculate the probability that it takes between 50 minutes and 100 minutes until the n eruption. (b) Calculate the 95th percentile of times between geyser eruptions. (c) Calculate the probability that the geyser will erupt at least once in the next 2 hours ( minutes). (d) How many times do you expect the geyser to erupt in the next 8 hours (480 minutes)? (e) Calculate the probability that the geyser will erupt exactly 4 times in the next 8 hours.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Great Geysers! The time (in minutes) between geyser eruptions can be modeled with an exponential distribution with mean 90 minutes (1.5 hours). (a) Calculate the probability that it takes between 50 minutes and 100 minutes until the next eruption. (b) Calculate the 95th percentile of times between geyser eruptions. (c) Calculate the probability that the geyser will erupt at least once in the next 2 hours (120 minutes). (d) How many times do you expect the geyser to erupt in the next 8 hours (480 minutes)? (e) Calculate the probability that the geyser will erupt exactly 4 times in the next 8 hours.
Transcribed Image Text:Great Geysers! The time (in minutes) between geyser eruptions can be modeled with an exponential distribution with mean 90 minutes (1.5 hours). (a) Calculate the probability that it takes between 50 minutes and 100 minutes until the next eruption. (b) Calculate the 95th percentile of times between geyser eruptions. (c) Calculate the probability that the geyser will erupt at least once in the next 2 hours (120 minutes). (d) How many times do you expect the geyser to erupt in the next 8 hours (480 minutes)? (e) Calculate the probability that the geyser will erupt exactly 4 times in the next 8 hours.
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