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Pest Control In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort," 500 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 20 of them had "checked in," while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out." Let 1 not checked in, and 2 = checked in.) (a) Set up the transition matrix P for the system with decimal entries. 0.96 0 Calculate p² 0.9216 0 0.04 1 0.0784 1 Calculate p3 0.884736 0 0.1168 x 1 (b) If a roach begins outside the "Resort," what is the probability of it "checking in" by the end of 1 hour? 2 hours? 3 hours? 1 hour 0.04 2 hours 0.0784 3 hours 0.1168 (c) What do you expect to be the long-term impact on the number of roaches? Eventually, all the roaches will have checked in. Eventually, all the roaches will not have checked in. There is not enough information.

Pest Control In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort," 500 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 20 of them had "checked in," while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out." Let 1 not checked in, and 2 = checked in.) (a) Set up the transition matrix P for the system with decimal entries. 0.96 0 Calculate p² 0.9216 0 0.04 1 0.0784 1 Calculate p3 0.884736 0 0.1168 x 1 (b) If a roach begins outside the "Resort," what is the probability of it "checking in" by the end of 1 hour? 2 hours? 3 hours? 1 hour 0.04 2 hours 0.0784 3 hours 0.1168 (c) What do you expect to be the long-term impact on the number of roaches? Eventually, all the roaches will have checked in. Eventually, all the roaches will not have checked in. There is not enough information.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 13CYU
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Pest Control In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort," 500 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 20 of them had "checked in," while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out." Let 1 not checked in, and 2 = checked in.) (a) Set up the transition matrix P for the system with decimal entries. 0.96 0 Calculate p² 0.9216 0 0.04 1 0.0784 1 Calculate p3 0.884736 0 0.1168 x 1 (b) If a roach begins outside the "Resort," what is the probability of it "checking in" by the end of 1 hour? 2 hours? 3 hours? 1 hour 0.04 2 hours 0.0784 3 hours 0.1168 (c) What do you expect to be the long-term impact on the number of roaches? Eventually, all the roaches will have checked in. Eventually, all the roaches will not have checked in. There is not enough information.
Transcribed Image Text:Pest Control In an experiment to test the effectiveness of the latest roach trap, the "Roach Resort," 500 roaches were placed in the vicinity of the trap and left there for an hour. At the end of the hour, it was observed that 20 of them had "checked in," while the rest were still scurrying around. (Remember that "once a roach checks in, it never checks out." Let 1 not checked in, and 2 = checked in.) (a) Set up the transition matrix P for the system with decimal entries. 0.96 0 Calculate p² 0.9216 0 0.04 1 0.0784 1 Calculate p3 0.884736 0 0.1168 x 1 (b) If a roach begins outside the "Resort," what is the probability of it "checking in" by the end of 1 hour? 2 hours? 3 hours? 1 hour 0.04 2 hours 0.0784 3 hours 0.1168 (c) What do you expect to be the long-term impact on the number of roaches? Eventually, all the roaches will have checked in. Eventually, all the roaches will not have checked in. There is not enough information.
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