The Mathematics Support Centre (M.S.C.) is a drop-in clinic, where students bring their queries regarding mathematical and statistical coursework. Students tend to visit the centre in small groups, typically comprised of three or fewer people. On average, eight groups of students arrive at the centre over the course of an hour.

Justifying your choice of distribution, calculate the probability that

at least six groups of students arrive within the next hour.

A new group of students has just arrived at the centre.

Each member of the group must register details of their visit, which takes some time.

Justifying your choice of distribution,

calculate the probability that the next group of students will arrive within three minutes.

Not all visitors to the M.S.C. can wait long enough to have their queries addressed by a tutor.

Over the course of a week, a survey is conducted.

Of the 425 students surveyed, 374 had their query addressed.

Calculate a 95% confidence interval for the proportion of queries that are addressed by tutors.

Interpret the meaning of a 95% confidence interval for the proportion.

[*Note from Rod*: the format of the context has been modified for legibility, because on some devices the sentences would have appeared to have been truncated.]