Suppose that a factory makes coins. For each coin, there is some p ∈(0,1) such that the probabitity oi tossing heads with that coin is p and the probability of tossing tails is 1 — p. Assume that a factory statistician notices that the parameter p roughly follows a normal distribution with mean 0.5 and standard deviation 0.1 . Then the probability that a randomly selected coin will land 3 consecutive heads lies in the interval (1/N+1, 1/N) for some positive integer N. What is N?