ALICE, a general purpose experiment designed to investigate nucleus-nucleus collisions at the CERN Large Hadron Collider (LHC), has also been used to detect atmospheric muons produced by cosmic-ray interactions in the atmosphere. In this contribution the analysis of the multiplicity distribution of the atmospheric muons detected by ALICE between 2010 and 2013 is presented, along with a comparison with Monte Carlo simulations. Special emphasis is given to the study of high-multiplicity events, i.e. those containing more than 100 reconstructed muons. Such high-multiplicity events demand primary cosmic rays with energy above $10^{16}$ eV. The frequency of these events can be successfully described by assuming a heavy mass composition of primary cosmic rays in this energy range, using the most recent interaction models to describe the development of the air shower resulting from the primary interaction.
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