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 × 10-6) Estimated Magnetic Susceptibility 0

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What is the value of λ?
λ =

(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.)


(c) Use the Poisson distribution to approximate the probability that the archaeologists will find more than eleven "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 x 10-6 (cmg × 10-6)
Estimated
Magnetic
Susceptibility
0 <x < 10
Number of
Probability
30/120 = 0.25
54/120 = 0.45
24/120 = 0.20
6/120 = 0.05
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
Comment
"cool"
Readings
30
"neutral"
10 < x < 20
54
"warm"
"very interesting"
"hot spot"
20 < x < 30
24
30 < x < 40
40 < x
6.
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.
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 × 10-6) Estimated Magnetic Susceptibility 0 <x < 10 Number of Probability 30/120 = 0.25 54/120 = 0.45 24/120 = 0.20 6/120 = 0.05 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 Comment "cool" Readings 30 "neutral" 10 < x < 20 54 "warm" "very interesting" "hot spot" 20 < x < 30 24 30 < x < 40 40 < x 6. 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.
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