In a village having more than 100 adults, eight are randomly selected in order to form a committee of residents. \(40 \%\) of adults in the village are connected with agriculture.

a. Verify that the guidelines have been satisfied about the relative sizes of the population and the sample, thus allowing the use of a binomial probability distribution for the number of selected adults connected with agriculture.

b. Check whether the guideline was satisfied for this binomial distribution to be reasonably approximated by a normal distribution.