Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 ( x < 20). Suppose n = 65 geomagnetic readings are taken. Let r be a binomial random variable that represents the number of "neutral" geomagnetic readings.

(a) We want to approximate the binomial random variable r by a normal variable x. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain.

(b) What is the probability that there will be at least 20 "neutral" readings out of these 65 trials?

(c) Why would the Poisson approximation to the binomial not be appropriate in this case? Explain.