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Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second × 10-6 (cmg × 10-6) Magnetic Susceptibility OSx< 10 10 sx< 20 20 sx < 30 Number of Readings Comment "col "neutral" "warm" "very interesting" "hot spot" Estimated Probability 30/120 = 0.25 54/120 = 0.45 18/120 = 0.15 12/120 = 0.10 6/120 = 0.05 30 54 18 30 sx< 40 12 40 5 and ng > 5 are both satisfied. O Yes, it is appropriate since the criteria n 2 100 and np < 10 are are both satisfied. O No, it is not appropriate since at least one of the criteria n 2 100 or np < 10 are not satisfied. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n 2 30. What is the value of 2? = (b) Use the Poisson distribution to approximate the probability that the archaeologists will find four or fewer "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.) (c) Use the Poisson distribution to approximate the probability that the archaeologists will find more than eight "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)

Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second × 10-6 (cmg × 10-6) Magnetic Susceptibility OSx< 10 10 sx< 20 20 sx < 30 Number of Readings Comment "col "neutral" "warm" "very interesting" "hot spot" Estimated Probability 30/120 = 0.25 54/120 = 0.45 18/120 = 0.15 12/120 = 0.10 6/120 = 0.05 30 54 18 30 sx< 40 12 40 5 and ng > 5 are both satisfied. O Yes, it is appropriate since the criteria n 2 100 and np < 10 are are both satisfied. O No, it is not appropriate since at least one of the criteria n 2 100 or np < 10 are not satisfied. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n 2 30. What is the value of 2? = (b) Use the Poisson distribution to approximate the probability that the archaeologists will find four or fewer "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.) (c) Use the Poisson distribution to approximate the probability that the archaeologists will find more than eight "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below.

Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second x 10-6 (cmg x 10-6) Magnetic Susceptibility 0 <x < 10 10 < x < 20 20 < x < 30 30 < x < 40 40 <x Number of Readings Estimated Probability 30/120 = 0.25 54/120 = 0.45 18/120 = 0.15 12/120 = 0.10 6/120 = 0.05 Comment "cool" "neutral" "warm" 30 54 18 "very interesting" "hot spot" 12 Suppose an archaeologist is looking for geomagnetic "hot spots" in an unexplored region. We have a binomial setting where success is a "hot spot." In this case, the probability of success is p = P(40 < x). The archaeologist takes n = 100 magnetic susceptibility readings in the new, unexplored area. Let r be a binomial random variable representing the number of "hot spots" in the 100 readings. (a) We want to approximate the binomial random variable r by a Poisson distribution. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied. O Yes, it is appropriate since the criteria n 2 100 and np < 10 are are both satisfied. O No, it is not appropriate since at least one of the criteria n2 100 or np < 10 are not satisfied. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n > 30. What is the value of 2? (b) Use the Poisson distribution to approximate the probability that the archaeologists will find four or fewer "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.) (c) Use the Poisson distribution to approximate the probability that the archaeologists will find more than eight "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)
Transcribed Image Text:Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second x 10-6 (cmg x 10-6) Magnetic Susceptibility 0 <x < 10 10 < x < 20 20 < x < 30 30 < x < 40 40 <x Number of Readings Estimated Probability 30/120 = 0.25 54/120 = 0.45 18/120 = 0.15 12/120 = 0.10 6/120 = 0.05 Comment "cool" "neutral" "warm" 30 54 18 "very interesting" "hot spot" 12 Suppose an archaeologist is looking for geomagnetic "hot spots" in an unexplored region. We have a binomial setting where success is a "hot spot." In this case, the probability of success is p = P(40 < x). The archaeologist takes n = 100 magnetic susceptibility readings in the new, unexplored area. Let r be a binomial random variable representing the number of "hot spots" in the 100 readings. (a) We want to approximate the binomial random variable r by a Poisson distribution. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied. O Yes, it is appropriate since the criteria n 2 100 and np < 10 are are both satisfied. O No, it is not appropriate since at least one of the criteria n2 100 or np < 10 are not satisfied. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n > 30. What is the value of 2? (b) Use the Poisson distribution to approximate the probability that the archaeologists will find four or fewer "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.) (c) Use the Poisson distribution to approximate the probability that the archaeologists will find more than eight "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)
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