According to Th e Scottish Government’s website, the average class size in publicly funded primary schools in Scotland had been declining over the years and is currently set at 23 students per class. Whilst most primary schools (52%) have classes of up to 25 students, a sizeable number of schools (16%) still have classes with 30 or more students. Suppose a complete list of class sizes in all Scottish publicly funded primary schools is available and 18 are randomly selected from that list.

a. What is the expected number of primary schools that have an average class size of up to 25 students? What is the expected number of schools with an average class size of 30 or more?

b. What is the probability that at least eight primary schools have an average class size of up to 25 students?

c. What is the probability that two, three, or four primary schools have an average class size of up to 25 students?

d. What is the probability that none of the public schools have an average class size of up to 25 students? What is the probability that none have an average class size of 30 or more? Which probability is higher and why?