  Multiple choice questions (MCQs) are commonly used for assessment in higher
education. With increased use of on-line examination it is likely that the
usage of MCQs will be even more in years to come. It is therefore of interest
to examine some characteristics of these type of questions such as the effect
of the number of distractors used and the "None of the above" (NOTA) or "All of
the above" (AOTA) options.
  The tutor-web is an open-source, on-line drilling system that is freely
available to anyone having access to the Internet. The system was designed to
be used for teaching mathematics and statistics but can in principle be used
for other subjects as well. The system offers thousands of multiple choice
questions at high school and university level. In addition to be a tool used by
students for learning it has also been used as a testbed for research on
web-assisted education.
  The tutor-web system was used both as a learning tool and as a testing tool
in a university course on mathematical statistics in the spring of 2020. Around
300 students were enrolled in the course providing tens of thousands of answers
to MCQs designed to investigate the effect of the number of distractors and the
use of NOTA and AOTA options in questions. The main findings of the study were
that the probability of answering a question correctly was highest when a AOTA
option was used as a distractor and when NOTA and AOTA were not used in
questions. The probability of answering a question correctly decreased with the
number of distractors.
