Question

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 archaeclogical research location. A random sample of 120 sites gave the readings shown in the table below Magnetic Susceptibility Readings, centimeter-gram-second x 10 (cmg Magnetic Susceptibility 0SK10 10 Sx<20 20 Sx30 30 x40 40 S x 10-6) Number of Readings 30 Estimated Probability 30/120 0.2S 54/120 0.45 18/120 0.15 12/120 0.10 6/120 0.05 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 probabilitys of success is p P40 x). The archaeologist takes n 100 magnetic susceptibility readings in the new, unexplored area. Let r be a binomial random variable representing Comment "cool "neutral warm "very interesting "hot spot 54 18 12 6 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 satisfled before we can do this? Do you think these requirements are satisfied in this case? Explain. No, it is not appropriate since at least one of the criteria np > 5 and ng> 5 are not satisfied. Yes, it is appropriate since n 30 No, it is not appropriate since at least ohe of the criteria n 2 100 or np< 10 are not satisfied. O Yes, it is appropriate since the criteria na 100 and np < 10 are are both satisfied. Yes, it is appropriate since the criteria np> 5 and ng> 5 are both satisfied. What is the value of A (b) Use the Poisson distribution to approximate the probability that the archaeologists will find six 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 seven "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)