Magnetic surveying is a technique used by archaeologists to identify anomalies due to variations in magnetic susceptibility. Changes in magnetic susceptibility may indicate potential archaeological discoveries. Here, \( x \) represents a magnetic susceptibility (MS) reading for a site at an archaeological location. A sample of 120 sites yielded the readings below:**Magnetic Susceptibility Readings:**| Comment | Magnetic Susceptibility (cmg x 10^–6) | Number of Readings | Estimated Probability ||-----------------|---------------------------------------|--------------------|-----------------------|| "cool" | 0 ≤ x < 10 | 30 | 30/120 = 0.25 || "neutral" | 10 ≤ x < 20 | 54 | 54/120 = 0.45 || "warm" | 20 ≤ x < 30 | 12 | 12/120 = 0.10 || "very interesting" | 30 ≤ x < 40 | 18 | 18/120 = 0.15 || "hot spot" | 40 ≤ x | 6 | 6/120 = 0.05 |Suppose an archaeologist is searching for geomagnetic "hot spots" (high readings) in an unexplored region. Here, a successful find is classified as a "hot spot." Let \( r \) be the binomial random variable representing the number of "hot spots" found in 100 readings, with success probability \( p = P(40 ≤ x) \).**Questions and Requirements:**(a) To approximate the binomial random variable \( r \) using a Poisson distribution:- **Which Statement is Correct?** - [ ] No, it is not appropriate since at least one of the criteria \( n \geq 100 \) or \( np < 10 \) are not satisfied. - [ ] No, it is not appropriate since at least one of the criteria \( np > 5 \) and \( nq > 5 \) are not satisfied. - [ ] Yes, it is appropriate since the criteria \( n \geq 100 \) and \( np < 10 \) are both satisfied. - [ ] Yes, it is appropriate since \( n \geq 30 \). - [ ] Yes

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 Magnetic Susceptibility 0sx < 10 10 s x < 20 20 s x < 30 30 < x < 40 40 < x (cmg x 10¬6) Number of Estimated Probability 30/120 = 0.25 54/120 = 0.45 12/120 = 0.10 18/120 = 0.15 6/120 = 0.05 Comment Readings 30 "cool" "neutral" 54 "warm" 12 "very interesting" "hot spot" 18 6 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 variabler 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 No, it is not appropriate since at least one of the criteria n > 100 or np < 10 are not satisfied. O No, it is not appropriate since at least one of the criteria np > 5 and nq > 5 are not satisfied. Yes, it is appropriate since the criteria n 2 100 and np < 10 are are both satisfied. O Yes, it is appropriate since n 2 30. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied. What is the value of 2? (b) Use the Poisson distribution to approximate the probability that the archaeologists will find five or fewer "hot spots." Hint: Use Table 4 of Appendix II. (Round your answer to four decimal places.)