Suppose an archaeologist is looking for geomagnetic "hot spots" in an unexplored region of Tara. As in Problem 8, 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. What is the value of l?

(b) What is the probability that the archaeologists will find six or fewer "hot spots?" Use Table 4 of Appendix II.

(c) What is the probability that the archaeologists will find more than eight "hot spots"?