Statistics Question finding the probability of a probability

Question

The question is "Women comprise 80.3% of all elementary school teachers. In a random sample of 300 elementary teachers, what is the probability that less than three-fourth are women?" I need to see the work done as well. Thanks a bunch

Answer 1

assuming no transexual issues

then it's a binomial distribution, each is either male or female

mean = np with p=probability of females= .803, q = 1-p = probability of males= .197, n=300

variance = npq

sd = sqr(npq)

calculate z value and use z tables or a statistics calculator to find probability