At a high school with 800 students, 80% of the students ride the school bus. if 20 students are selected randomly (without replacement) and we let x = the number of students in the sample who ride the bus, then x does not exactly have a binomial distribution. why is it nevertheless appropriate to approximate probabilities for x using the binomial distribution for n = 20 and p = 0.8? the binomial is always appropriate when sampling without replacement. because the sample is less than 10% of the population, it is appropriate to use the binomial distribution even though the samples are not strictly independent. since np > 10, we can still use the binomial distribution. next