This problem illustrates the limit derivation of a Poisson distribution from Binomial distributions. Suppose an average of 66 arrivals occur during a 30 minute interval. To count arrivals, divide the 30 minute interval into nn sub-intervals. On the previous problem, you found the probability pp of one arrival during a single sub-interval for each n given. Now, compute the (estimated) probability that there will be, in fact, exactly 6 arrivals during a 30 minute interval, with each probability model: a. Using Binomial with n=30, the chance of 6 arrivals is estimated as:
b. Using Binomial with n=60, the chance of 6 arrivals is estimated as:
c. Using Binomial with n=100n=100, the chance of 6 arrivals is estimated as:
d. Using Poisson, the chance of 6 arrivals is estimated as:

Required:
Use a probability calculator, and enter answers in decimal form, rounded to at least four places after the decimal.