Suppose 6% of dolphins in a particular population are observed to be traveling each morning. There are 100 dolphins in this population.

a) Assuming that whether a dolphin is traveling on a particular morning is a random variable independent of whether any other dolphin is traveling, what is the mean and variance of the number of dolphins traveling on any particular morning?

b) Calculate the probability that the number of dolphins traveling on a given morning is greater than 5,

(i) using the exact binomial distribution,

(ii) using the Poisson distribution with the same mean,

(iii) using the normal distribution with the same mean and variance.

c) Is either approximation valid? Is either approximation useful? Justify your answer.